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29556478 | 10.1007/s00029-016-0236-z | We study some aspects of modular generalized Springer theory for a complex
reductive group $G$ with coefficients in a field $\mathbb k$ under the
assumption that the characteristic $\ell$ of $\mathbb k$ is rather good for
$G$, i.e., $\ell$ is good and does not divide the order of the component group
of the centre of $G$. We prove a comparison theorem relating the
characteristic-$\ell$ generalized Springer correspondence to the
characteristic-$0$ version. We also consider Mautner's characteristic-$\ell$
`cleanness conjecture'; we prove it in some cases; and we deduce several
consequences, including a classification of supercuspidal sheaves and an
orthogonal decomposition of the equivariant derived category of the nilpotent
cone.Comment: 26 page | Constructible sheaves on nilpotent cones in rather good characteristic | constructible sheaves on nilpotent cones in rather good characteristic | modular springer reductive mathbb mathbb i.e. divide relating springer correspondence version. mautner cleanness conjecture deduce consequences supercuspidal sheaves orthogonal decomposition equivariant nilpotent | non_dup | [] |
25063073 | 10.1007/s00029-016-0241-2 | We introduce the Tesler polytope Tes_n(a_1,a_2,...,a_n), whose integer points
are the Tesler matrices of size n with nonnegative integer hook sums
a_1,a_2,...,a_n. We show that Tes_n(a) is a flow polytope and therefore the
number of Tesler matrices is counted by the type A_n Kostant partition function
evaluated at (a_1,a_2,...,a_n,-a_1-...-a_n). We describe the faces of this
polytope in terms of "Tesler tableaux" and characterize when the polytope is
simple. We prove that the h-vector of Tes_n(a) when all a_i>0 is given by the
Mahonian numbers and calculate the volume of Tes_n(1,1,...,1) to be a product
of consecutive Catalan numbers multiplied by the number of standard Young
tableaux of staircase shape.Comment: 26 pages, 4 figures. v3 has a corrected proof of Lemma 2.4, updated
reference | The polytope of Tesler matrices | the polytope of tesler matrices | tesler polytope integer tesler nonnegative integer hook sums polytope tesler counted kostant partition faces polytope tesler tableaux characterize polytope simple. mahonian consecutive catalan multiplied tableaux staircase pages figures. corrected updated | non_dup | [] |
42651291 | 10.1007/s00029-016-0259-5 | Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and
Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from
the category of smooth modulo $p^n$ representations of $B$ to the category of
projective limits of finitely generated \'etale $(\varphi,\Gamma)$-modules over
a multivariable (indexed by the set of simple roots) commutative Laurent-series
ring. These correspond to representations of a direct power of
$\mathrm{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)$ via an equivalence of
categories. Parabolic induction from a subgroup $P=L_PN_P$ corresponds to a
basechange from a Laurent-series ring in those variables with corresponding
simple roots contained in the Levi component $L_P$. $D^\vee_\Delta$ is exact
and yields finitely generated objects on the category $SP_A$ of finite length
representations with subquotients of principal series as Jordan-H\"older
factors. Lifting the functor $D^\vee_\Delta$ to all (noncommuting) variables
indexed by the positive roots allows us to construct a $G$-equivariant sheaf
$\mathfrak{Y}_{\pi,\Delta}$ on $G/B$ and a $G$-equivariant continuous map from
the Pontryagin dual $\pi^\vee$ of a smooth representation $\pi$ of $G$ to the
global sections $\mathfrak{Y}_{\pi,\Delta}(G/B)$. We deduce that
$D^\vee_\Delta$ is fully faithful on the full subcategory of $SP_A$ with
Jordan-H\"older factors isomorphic to irreducible principal series.Comment: 55 pages, revised, to appear in Selecta Mathematic | Multivariable $(\varphi,\Gamma)$-modules and smooth $o$-torsion
representations | multivariable $(\varphi,\gamma)$-modules and smooth $o$-torsion representations | mathbb split reductive borel subgroup functor delta modulo representations projective finitely etale varphi gamma modules multivariable indexed roots commutative laurent ring. representations mathrm overline mathbb mathbb equivalence categories. parabolic subgroup basechange laurent roots levi delta finitely representations subquotients principal jordan older factors. lifting functor delta noncommuting indexed roots equivariant sheaf mathfrak delta equivariant pontryagin mathfrak delta deduce delta faithful subcategory jordan older isomorphic irreducible principal pages revised selecta mathematic | non_dup | [] |
24997734 | 10.1007/s00029-016-0264-8 | In 1998, Leclerc and Zelevinsky introduced the notion of weakly separated
collections of subsets of the ordered $n$-element set $[n]$ (using this notion
to give a combinatorial characterization for quasi-commuting minors of a
quantum matrix). They conjectured the purity of certain natural domains
$D\subseteq 2^{[n]}$ (in particular, of the hypercube $2^{[n]}$ itself, and the
hyper-simplex $\{X\subseteq[n]\colon |X|=m\}$ for $m$ fixed), where $D$ is
called pure if all maximal weakly separated collections in $D$ have the same
cardinality. These conjectures have been answered affirmatively.
In this paper, generalizing those earlier results, we reveal wider classes of
pure domains in $2^{[n]}$. This is obtained as a consequence of our study of a
novel geometric--combinatorial model for weakly separated set-systems,
so-called \emph{combined (polygonal) tilings} on a zonogon, which yields a new
insight in the area.Comment: 30 pages. Revised version. To appear in Selecta Mathematic | Combined tilings and separated set-systems | combined tilings and separated set-systems | leclerc zelevinsky notion weakly separated collections subsets ordered notion combinatorial quasi commuting minors conjectured purity subseteq hypercube hyper simplex subseteq colon maximal weakly separated collections cardinality. conjectures answered affirmatively. generalizing reveal wider geometric combinatorial weakly separated emph polygonal tilings zonogon insight pages. revised version. selecta mathematic | non_dup | [] |
25043340 | 10.1007/s00029-016-0266-6 | We study a class of scalar, linear, non-local Riemann-Hilbert problems (RHP)
involving finite subgroups of PSL(2,C). We associate to such problems a (maybe
infinite) root system and describe the relevance of the orbits of the Weyl
group in the construction of its solutions. As an application, we study in
detail the large N expansion of SU(N) or SO(N) or Sp(2N) Chern-Simons partition
function Z_N(M) of 3-manifolds M that are either rational homology spheres or
more generally Seifert fibered spaces. It has a matrix model-like
representation, whose spectral curve can be characterized in terms of a RHP as
above. When pi_1(M) is finite (i.e. for manifolds M that are quotients of
\mathbb{S}_{3} by a finite isometry group of type ADE), the Weyl group
associated to the RHP is finite and the spectral curve is algebraic and can be
in principle computed. We then show that the large $N$ expansion of Z_N(M) is
computed by the topological recursion. This has consequences for the
analyticity properties of SU/SO/Sp perturbative invariants of knots along
fibers in $M$.Comment: 92 pages, 20 figures. Section 9 by Alexander Wei{\ss} | Root systems, spectral curves, and analysis of a Chern-Simons matrix
model for Seifert fibered spaces | root systems, spectral curves, and analysis of a chern-simons matrix model for seifert fibered spaces | riemann hilbert involving subgroups associate maybe infinite relevance orbits weyl solutions. chern simons partition manifolds rational homology spheres seifert fibered spaces. above. i.e. manifolds quotients mathbb isometry weyl algebraic computed. topological recursion. consequences analyticity perturbative invariants knots fibers .comment pages figures. alexander | non_dup | [] |
42673693 | 10.1007/s00029-016-0280-8 | We prove that the dg category of perfect complexes on a smooth, proper
Deligne-Mumford stack over a field of characteristic zero is geometric in the
sense of Orlov, and in particular smooth and proper. On the level of
triangulated categories, this means that the derived category of perfect
complexes embeds as an admissible subcategory into the bounded derived category
of coherent sheaves on a smooth, projective variety. The same holds for a
smooth, projective, tame Artin stack over an arbitrary field.Comment: 31 page | Geometricity for derived categories of algebraic stacks | geometricity for derived categories of algebraic stacks | perfect complexes proper deligne mumford stack geometric orlov proper. triangulated categories perfect complexes embeds admissible subcategory coherent sheaves projective variety. projective tame artin stack | non_dup | [] |
29534677 | 10.1007/s00029-016-0285-3 | Schwartz functions, or measures, are defined on any smooth semi-algebraic
("Nash") manifold, and are known to form a cosheaf for the semi-algebraic
restricted topology. We extend this definition to smooth semi-algebraic stacks,
which are defined as geometric stacks in the category of Nash manifolds.
Moreover, when those are obtained from algebraic quotient stacks of the form
X/G, with X a smooth affine variety and G a reductive group defined over a
global field k, we define, whenever possible, an "evaluation map" at each
semisimple k-point of the stack, without using truncation methods. This
corresponds to a regularization of the sum of those orbital integrals whose
semisimple part corresponds to the chosen k-point.
These evaluation maps produce, in principle, a distribution which generalizes
the Arthur-Selberg trace formula and Jacquet's relative trace formula, although
the former, and many instances of the latter, cannot actually be defined by the
purely geometric methods of this paper. In any case, the stack-theoretic point
of view provides an explanation for the pure inner forms that appear in many
versions of the Langlands, and relative Langlands, conjectures.Comment: 96pp. Erratum added at the end to fix two gaps and strengthen some
statements from quasi-isomorphism to homotopy equivalenc | The Schwartz space of a smooth semi-algebraic stack | the schwartz space of a smooth semi-algebraic stack | schwartz algebraic nash manifold cosheaf algebraic restricted topology. extend algebraic stacks geometric stacks nash manifolds. algebraic quotient stacks affine reductive whenever semisimple stack truncation methods. regularization orbital integrals semisimple point. generalizes arthur selberg trace jacquet trace former instances purely geometric paper. stack theoretic explanation versions langlands langlands erratum gaps strengthen statements quasi isomorphism homotopy equivalenc | non_dup | [] |
29529746 | 10.1007/s00029-016-0287-1 | We study a moduli problem on a nodal curve of arithmetic genus 1, whose
solution is an open subscheme in the zastava space for projective line. This
moduli space is equipped with a natural Poisson structure, and we compute it in
a natural coordinate system. We compare this Poisson structure with the
trigonometric Poisson structure on the transversal slices in an affine flag
variety. We conjecture that certain generalized minors give rise to a cluster
structure on the trigonometric zastava.Comment: Main text by M. Finkelberg, A. Kuznetsov and L. Rybnikov with an
appendix by G. Dobrovolska; v3 32 pages, Proof of Proposition 4.3 corrected,
Section 1.5 added; v4 33 pages, the final version to appear in Selecta Math.;
v5 the published versio | Towards a cluster structure on trigonometric zastava | towards a cluster structure on trigonometric zastava | moduli nodal arithmetic genus subscheme zastava projective line. moduli equipped poisson coordinate system. poisson trigonometric poisson transversal slices affine flag variety. conjecture minors trigonometric finkelberg kuznetsov rybnikov dobrovolska pages corrected pages selecta math. versio | non_dup | [] |
29524841 | 10.1007/s00029-016-0290-6 | For a left coherent ring A with every left ideal having a countable set of
generators, we show that the coderived category of left A-modules is compactly
generated by the bounded derived category of finitely presented left A-modules
(reproducing a particular case of a recent result of Stovicek with our
methods). Furthermore, we present the definition of a dualizing complex of
fp-injective modules over a pair of noncommutative coherent rings A and B, and
construct an equivalence between the coderived category of A-modules and the
contraderived category of B-modules. Finally, we define the notion of a
relative dualizing complex of bimodules for a pair of noncommutative ring
homomorphisms A \to R and B \to S, and obtain an equivalence between the
R/A-semicoderived category of R-modules and the S/B-semicontraderived category
of S-modules. For a homomorphism of commutative rings A\to R, we also construct
a tensor structure on the R/A-semicoderived category of R-modules. A vision of
semi-infinite algebraic geometry is discussed in the introduction.Comment: LaTeX 2e with pb-diagram and xy-pic, 30 pages, 2 commutative
diagrams; v.3: several misprints corrected, expositional improvement in
Section 2; v.4: examples added in the introduction and in Sections 3 and 5;
v.5: more misprints corrected, new Section 6 added; v.6: exposition improved
in Section 6 -- this is intended as the final versio | Coherent rings, fp-injective modules, dualizing complexes, and covariant
Serre-Grothendieck duality | coherent rings, fp-injective modules, dualizing complexes, and covariant serre-grothendieck duality | coherent ideal countable generators coderived modules compactly finitely modules reproducing stovicek dualizing injective modules noncommutative coherent rings equivalence coderived modules contraderived modules. notion dualizing bimodules noncommutative homomorphisms equivalence semicoderived modules semicontraderived modules. homomorphism commutative rings semicoderived modules. vision infinite algebraic latex pages commutative diagrams misprints corrected expositional misprints corrected exposition intended versio | non_dup | [] |
42680592 | 10.1007/s00029-016-0293-3 | We study Quot schemes of 0-dimensional quotients of sheaves on 3-folds $X$.
When the sheaf $\mathcal{R}$ is rank 2 and reflexive, we prove that the
generating function of Euler characteristics of these Quot schemes is a power
of the MacMahon function times a polynomial. This polynomial is itself the
generating function of Euler characteristics of Quot schemes of a certain
0-dimensional sheaf, which is supported on the locus where $\mathcal{R}$ is not
locally free.
In the case $X = \mathbb{C}^3$ and $\mathcal{R}$ is equivariant, we use our
result to prove an explicit product formula for the generating function. This
formula was first found using localization techniques in previous joint work
with B. Young. Our results follow from R. Hartshorne's Serre correspondence and
a rank 2 version of a Hall algebra calculation by J. Stoppa and R.P. Thomas.Comment: 20 pages. Published version. Addition to published version: the
assumptions in Thm. 1.2 can be weakened due to an argument from J. Rennemo
(Section 1.2 | Rank 2 wall-crossing and the Serre correspondence | rank 2 wall-crossing and the serre correspondence | quot schemes quotients sheaves folds sheaf mathcal reflexive generating euler quot schemes macmahon polynomial. generating euler quot schemes sheaf locus mathcal locally free. mathbb mathcal equivariant generating function. localization young. hartshorne serre correspondence hall stoppa r.p. pages. version. assumptions thm. weakened argument rennemo | non_dup | [] |
42676587 | 10.1007/s00029-016-0295-1 | In this paper, we continue the study of the existence problem of compact
Clifford-Klein forms from a cohomological point of view, which was initiated by
Kobayashi-Ono and extended by Benoist-Labourie and the author. We give an
obstruction to the existence of compact Clifford-Klein forms by relating a
natural homomorphism from relative Lie algebra cohomology to de Rham cohomology
with an upper-bound estimate for cohomological dimensions of discontinuous
groups. From this obstruction, we derive some examples, e.g.
$\mathrm{SO}_0(p+r, q)/(\mathrm{SO}_0(p,q) \times \mathrm{SO}(r))$ $(p,q,r \geq
1, \ q:\text{odd})$ and $\mathrm{SL}(p+q, \mathbb{C})/\mathrm{SU}(p,q)$ $(p,q
\geq 1)$, of a homogeneous space that does not admit a compact Clifford-Klein
form. To construct these examples, we apply H. Cartan's theorem on relative Lie
algebra cohomology of reductive pairs and the theory of $\epsilon$-families of
semisimple symmetric pairs.Comment: 18 page | A cohomological obstruction to the existence of compact Clifford-Klein
forms | a cohomological obstruction to the existence of compact clifford-klein forms | continue clifford klein cohomological initiated kobayashi benoist labourie author. obstruction clifford klein relating homomorphism cohomology rham cohomology cohomological discontinuous groups. obstruction derive e.g. mathrm mathrm mathrm mathrm mathbb mathrm homogeneous admit clifford klein form. cartan cohomology reductive epsilon families semisimple | non_dup | [] |
42680112 | 10.1007/s00029-016-0296-0 | We prove that a universal class categorical in a high-enough cardinal is
categorical on a tail of cardinals. As opposed to other results in the
literature, we work in ZFC, do not require the categoricity cardinal to be a
successor, do not assume amalgamation, and do not use large cardinals. Moreover
we give an explicit bound on the "high-enough" threshold:
$\mathbf{Theorem}$
Let $\psi$ be a universal $\mathbb{L}_{\omega_1, \omega}$ sentence. If $\psi$
is categorical in some $\lambda \ge \beth_{\beth_{\omega_1}}$, then $\psi$ is
categorical in all $\lambda' \ge \beth_{\beth_{\omega_1}}$.
As a byproduct of the proof, we show that a conjecture of Grossberg holds in
universal classes:
$\mathbf{Corollary}$
Let $\psi$ be a universal $\mathbb{L}_{\omega_1, \omega}$ sentence that is
categorical in some $\lambda \ge \beth_{\beth_{\omega_1}}$, then the class of
models of $\psi$ has the amalgamation property for models of size at least
$\beth_{\beth_{\omega_1}}$.
We also establish generalizations of these two results to uncountable
languages. As part of the argument, we develop machinery to transfer
model-theoretic properties between two different classes satisfying a
compatibility condition. This is used as a bridge between Shelah's milestone
study of universal classes (which we use extensively) and a categoricity
transfer theorem of the author for abstract elementary classes that have
amalgamation, are tame, and have primes over sets of the form $M \cup \{a\}$.Comment: 49 page | Shelah's eventual categoricity conjecture in universal classes. Part II | shelah's eventual categoricity conjecture in universal classes. part ii | universal categorical cardinal categorical tail cardinals. opposed categoricity cardinal successor amalgamation cardinals. mathbf universal mathbb omega omega sentence. categorical lambda beth beth omega categorical lambda beth beth omega byproduct conjecture grossberg universal mathbf corollary universal mathbb omega omega sentence categorical lambda beth beth omega amalgamation beth beth omega establish generalizations uncountable languages. argument machinery theoretic satisfying compatibility condition. bridge shelah milestone universal extensively categoricity elementary amalgamation tame primes .comment | non_dup | [] |
42691950 | 10.1007/s00029-017-0302-1 | The topological vertex is a universal series which can be regarded as an
object in combinatorics, representation theory, geometry, or physics. It
encodes the combinatorics of 3D partitions, the action of vertex operators on
Fock space, the Donaldson-Thomas theory of toric Calabi-Yau threefolds, or the
open string partition function of $\mathbb{C}^3$.
We prove several identities in which a sum over terms involving the
topological vertex is expressed as a closed formula, often a product of simple
terms, closely related to Fourier expansions of Jacobi forms. We use purely
combinatorial and representation theoretic methods to prove our formulas, but
we discuss applications to the Donaldson-Thomas invariants of elliptically
fibered Calabi-Yau threefolds at the end of the paper.Comment: 21 page | Trace Identities for the Topological Vertex | trace identities for the topological vertex | topological universal regarded combinatorics physics. encodes combinatorics partitions fock donaldson thomas toric calabi threefolds partition mathbb identities involving topological closely fourier expansions jacobi forms. purely combinatorial theoretic formulas donaldson thomas invariants elliptically fibered calabi threefolds | non_dup | [] |
29501489 | 10.1007/s00029-017-0314-x | We call a knot in the 3-sphere $SU(2)$-simple if all representations of the
fundamental group of its complement which map a meridian to a trace-free
element in $SU(2)$ are binary dihedral. This is a generalisation of being a
2-bridge knot. Pretzel knots with bridge number $\geq 3$ are not
$SU(2)$-simple. We provide an infinite family of knots $K$ with bridge number
$\geq 3$ which are $SU(2)$-simple.
One expects the instanton knot Floer homology $I^\natural(K)$ of a
$SU(2)$-simple knot to be as small as it can be -- of rank equal to the knot
determinant $\det(K)$. In fact, the complex underlying $I^\natural(K)$ is of
rank equal to $\det(K)$, provided a genericity assumption holds that is
reasonable to expect. Thus formally there is a resemblance to strong L-spaces
in Heegaard Floer homology. For the class of $SU(2)$-simple knots that we
introduce this formal resemblance is reflected topologically: The branched
double covers of these knots are strong L-spaces. In fact, somewhat
surprisingly, these knots are alternating. However, the Conway spheres are
hidden in any alternating diagram.
With the methods we use, we show that an integer homology 3-sphere which is a
graph manifold always admits irreducible representations of its fundamental
group.Comment: 22 pages, 10 figures, to appear in Selecta Mathematic | A class of knots with simple $SU(2)$ representations | a class of knots with simple $su(2)$ representations | call knot sphere representations complement meridian trace dihedral. generalisation bridge knot. pretzel knots bridge simple. infinite knots bridge simple. expects instanton knot floer homology knot knot determinant genericity reasonable expect. formally resemblance heegaard floer homology. knots formal resemblance reflected topologically branched covers knots spaces. somewhat surprisingly knots alternating. conway spheres hidden alternating diagram. integer homology sphere manifold admits irreducible representations pages selecta mathematic | non_dup | [] |
42735742 | 10.1007/s00029-017-0315-9 | Let $\mathfrak{g}$ be a simple finite-dimensional Lie superalgebra with a
non-degenerate supersymmetric even invariant bilinear form, $f$ a nilpotent
element in the even part of $\mathfrak{g}$, $\Gamma$ a good grading of
$\mathfrak{g}$ for $f$ and $\mathcal{W}^{k}(\mathfrak{g},f;\Gamma)$ the
$\mathcal{W}$-algebra associated with $\mathfrak{g},f,k,\Gamma$ defined by the
generalized Drinfeld-Sokolov reduction. In this paper, we present each
$\mathcal{W}$-algebra as the intersection of kernels of the screening
operators, acting on the tensor vertex superalgebra of an affine vertex
superalgebra and a neutral free superfermion vertex superalgebra. As
applications, we prove that the $\mathcal{W}$-algebra associated with a regular
nilpotent element in $\mathfrak{osp}(1,2n)$ is isomorphic to the
$\mathcal{W}B_{n}$-algebra introduced by Fateev and Lukyanov, and that the
$\mathcal{W}$-algebra associated with a subregular nilpotent element in
$\mathfrak{sl}_{n}$ is isomorphic to the $\mathcal{W}^{(2)}_{n}$-algebra
introduced by Feigin and Semikhatov.Comment: revised version, to appear in Sel. Math. New Se | Screening operators for W-algebras | screening operators for w-algebras | mathfrak superalgebra degenerate supersymmetric bilinear nilpotent mathfrak gamma grading mathfrak mathcal mathfrak gamma mathcal mathfrak gamma drinfeld sokolov reduction. mathcal intersection kernels screening acting superalgebra affine superalgebra neutral superfermion superalgebra. mathcal nilpotent mathfrak isomorphic mathcal fateev lukyanov mathcal subregular nilpotent mathfrak isomorphic mathcal feigin revised sel. math. | non_dup | [] |
42751172 | 10.1007/s00029-017-0316-8 | The goal of this work is to provide an elementary construction of the
canonical basis $\mathbf B(w)$ in each quantum Schubert cell~$U_q(w)$ and to
establish its invariance under modified Lusztig's symmetries. To that effect,
we obtain a direct characterization of the upper global basis $\mathbf B^{up}$
in terms of a suitable bilinear form and show that $\mathbf B(w)$ is contained
in $\mathbf B^{up}$ and its large part is preserved by modified Lusztig's
symmetries.Comment: AMSLaTeX, 32 pages,typos correcte | Canonical bases of quantum Schubert cells and their symmetries | canonical bases of quantum schubert cells and their symmetries | goal elementary canonical mathbf schubert establish invariance lusztig symmetries. mathbf bilinear mathbf mathbf preserved lusztig amslatex pages typos correcte | non_dup | [] |
42744748 | 10.1007/s00029-017-0319-5 | We look at Poisson geometry taking the viewpoint of singular foliations,
understood as suitable submodules generated by Hamiltonian vector fields rather
than partitions into (symplectic) leaves. The class of Poisson structures which
behave best from this point of view, are those whose submodule generated by
Hamiltonian vector fields arises from a smooth holonomy groupoid. We call them
almost regular Poisson structures and determine them completely. They include
regular Poisson and log symplectic manifolds, as well as several other Poisson
structures whose symplectic foliation presents singularities.
We show that the holonomy groupoid associated with an almost regular Poisson
structure is a Poisson groupoid, integrating a naturally associated Lie
bialgebroid. The Poisson structure on the holonomy groupoid is regular, and as
such it provides a desingularization. The holonomy groupoid is "minimal" among
Lie groupoids which give rise to the submodule generated by Hamiltonian vector
fields. This implies that, in the case of log-symplectic manifolds, the
holonomy groupoid coincides with the symplectic groupoid constructed by
Gualtieri and Li. Last, we focus on the integrability of almost regular Poisson
manifolds and exhibit the role of the second homotopy group of the
source-fibers of the holonomy groupoid.Comment: 36 pages. This version has been accepted for publicatio | Almost regular Poisson manifolds and their holonomy groupoids | almost regular poisson manifolds and their holonomy groupoids | look poisson viewpoint singular foliations understood submodules partitions symplectic leaves. poisson behave submodule arises holonomy groupoid. call poisson completely. poisson symplectic manifolds poisson symplectic foliation presents singularities. holonomy groupoid poisson poisson groupoid integrating naturally bialgebroid. poisson holonomy groupoid desingularization. holonomy groupoid groupoids submodule fields. symplectic manifolds holonomy groupoid coincides symplectic groupoid gualtieri integrability poisson manifolds exhibit homotopy fibers holonomy pages. publicatio | non_dup | [] |
29528919 | 10.1007/s00029-017-0324-8 | We present a new method of proving the Diophantine extremality of various
dynamically defined measures, vastly expanding the class of measures known to
be extremal. This generalizes and improves the celebrated theorem of Kleinbock
and Margulis ('98) resolving Sprind\v{z}uk's conjecture, as well as its
extension by Kleinbock, Lindenstrauss, and Weiss ('04), hereafter abbreviated
KLW. As applications we prove the extremality of all hyperbolic measures of
smooth dynamical systems with sufficiently large Hausdorff dimension, and of
the Patterson--Sullivan measures of all nonplanar geometrically finite groups.
The key technical idea, which has led to a plethora of new applications, is a
significant weakening of KLW's sufficient conditions for extremality.
In Part I, we introduce and develop a systematic account of two classes of
measures, which we call $quasi$-$decaying$ and $weakly$ $quasi$-$decaying$. We
prove that weak quasi-decay implies strong extremality in the matrix
approximation framework (which has received much attention in recent years),
thus proving a conjecture of KLW. We also prove the "inherited exponent of
irrationality" version of this theorem, describing the relationship between the
Diophantine properties of certain subspaces of the space of matrices and
measures supported on these subspaces.
In subsequent papers, we exhibit numerous examples of quasi-decaying
measures, in support of the thesis that "almost any measure from dynamics
and/or fractal geometry is quasi-decaying". In addition to the examples
described above, we also prove (for example) that Gibbs measures (including
conformal measures) of infinite iterated function systems are quasi-decaying,
even if the systems in question do not satisfy the open set condition. We also
discuss examples of non-extremal measures coming from dynamics, illustrating
where the theory must halt.Comment: Link to part II: arXiv:1508.0559 | Extremality and dynamically defined measures, part I: Diophantine
properties of quasi-decaying measures | extremality and dynamically defined measures, part i: diophantine properties of quasi-decaying measures | proving diophantine extremality dynamically vastly expanding extremal. generalizes improves celebrated kleinbock margulis resolving sprind conjecture kleinbock lindenstrauss weiss hereafter abbreviated klw. extremality hyperbolic sufficiently hausdorff patterson sullivan nonplanar geometrically groups. plethora weakening extremality. call quasi decaying weakly quasi decaying quasi extremality proving conjecture klw. inherited exponent irrationality describing diophantine subspaces subspaces. papers exhibit numerous quasi decaying thesis fractal quasi decaying gibbs conformal infinite iterated quasi decaying satisfy condition. extremal coming illustrating | non_dup | [] |
73388729 | 10.1007/s00029-017-0328-4 | We refine the statement of the denominator and evaluation conjectures for
affine Macdonald polynomials proposed by Etingof-Kirillov Jr. and prove the
first non-trivial cases of these conjectures. Our results provide a
q-deformation of the computation of genus 1 conformal blocks via elliptic
Selberg integrals by Felder-Stevens-Varchenko. They allow us to give precise
formulations for the affine Macdonald conjectures in the general case which are
consistent with computer computations.
Our method applies recent work of the second named author to relate these
conjectures in the case of $U_q(\widehat{\mathfrak{sl}}_2)$ to evaluations of
certain theta hypergeometric integrals defined by Felder-Varchenko. We then
evaluate the resulting integrals, which may be of independent interest, by
well-chosen applications of the elliptic beta integral introduced by
Spiridonov.Comment: 26 pages. v3: minor edits for published versio | Affine Macdonald conjectures and special values of Felder-Varchenko
functions | affine macdonald conjectures and special values of felder-varchenko functions | refine statement denominator conjectures affine macdonald polynomials etingof kirillov trivial conjectures. deformation genus conformal blocks elliptic selberg integrals felder stevens varchenko. precise formulations affine macdonald conjectures computations. applies named relate conjectures widehat mathfrak evaluations theta hypergeometric integrals felder varchenko. integrals elliptic beta pages. minor edits versio | non_dup | [] |
42678862 | 10.1007/s00029-017-0338-2 | We prove an inequality between the $L^{\infty}$-norm of the contact
Hamiltonian of a positive loop of contactomorphims and the minimal Reeb period.
This implies that there are no small positive loops on hypertight or Liouville
fillable contact manifolds. Non-existence of small positive loops for
overtwisted 3-manifolds was proved by Casals-Presas-Sandon in [CPS16].
As corollaries of the inequality we deduce various results. E.g. we prove
that certain periodic Reeb flows are the unique minimizers of the
$L^\infty$-norm. Moreover, we establish $L^\infty$-type contact systolic
inequalities in the presence of a positive loop.Comment: 26 pages, 6 figures; v2: corrected an error, changed statements of
main theorems; v3: accepted version, to appear in Selecta Mathematic | Positive loops and $L^{\infty}$-contact systolic inequalities | positive loops and $l^{\infty}$-contact systolic inequalities | inequality infty norm contactomorphims reeb period. loops hypertight liouville fillable manifolds. loops overtwisted manifolds proved casals presas sandon corollaries inequality deduce results. e.g. reeb flows minimizers infty norm. establish infty systolic inequalities pages corrected changed statements theorems selecta mathematic | non_dup | [] |
42664337 | 10.1007/s00029-017-0339-1 | We provide a construction of free factorization algebras in algebraic
geometry and link factorization homology of a scheme with coefficients in a
free factorization algebra to the homology of its (unordered) configuration
spaces. As an application, this construction allows for a purely
algebro-geometric proof of homological stability of configuration spaces.Comment: The final publication is available at Springer via
http://dx.doi.org/doi:10.1007/s00029-017-0339-1, Selecta Mathematica (N.S.)
201 | Free factorization algebras and homology of configuration spaces in
algebraic geometry | free factorization algebras and homology of configuration spaces in algebraic geometry | factorization algebras algebraic factorization homology factorization homology unordered spaces. purely algebro geometric homological publication springer selecta mathematica n.s. | non_dup | [] |
42667549 | 10.1007/s00029-017-0343-5 | We explore the relationship between a certain "abelian duality" property of
spaces and the propagation properties of their cohomology jump loci. To that
end, we develop the analogy between abelian duality spaces and those spaces
which possess what we call the "EPY property." The same underlying homological
algebra allows us to deduce the propagation of jump loci: in the former case,
characteristic varieties propagate, and in the latter, the resonance varieties.
We apply the general theory to arrangements of linear and elliptic hyperplanes,
as well as toric complexes, right-angled Artin groups, and Bestvina-Brady
groups. Our approach brings to the fore the relevance of the Cohen-Macaulay
condition in this combinatorial context.Comment: 30 page | Abelian duality and propagation of resonance | abelian duality and propagation of resonance | explore abelian duality propagation cohomology jump loci. analogy abelian duality possess call property. homological deduce propagation jump loci former varieties propagate varieties. arrangements elliptic hyperplanes toric complexes angled artin bestvina brady groups. brings fore relevance cohen macaulay combinatorial | non_dup | [] |
73958233 | 10.1007/s00029-017-0344-4 | We discuss a conjecture saying that derived equivalence of simply connected
smooth projective varieties implies that the difference of their classes in the
Grothendieck ring of varieties is annihilated by a power of the affine line
class.
We support the conjecture with a number of known examples, and one new
example. We consider a smooth complete intersection $X$ of three quadrics in
${\mathbf P}^5$ and the corresponding double cover $Y \to {\mathbf P}^2$
branched over a sextic curve. We show that as soon as the natural Brauer class
on $Y$ vanishes, so that $X$ and $Y$ are derived equivalent, the difference
$[X] - [Y]$ is annihilated by the affine line class.Comment: Exposition improved, main conjecture slightly update | Grothendieck ring of varieties, D- and L-equivalence, and families of
quadrics | grothendieck ring of varieties, d- and l-equivalence, and families of quadrics | conjecture saying equivalence projective varieties grothendieck varieties annihilated affine class. conjecture example. intersection quadrics mathbf cover mathbf branched sextic curve. soon brauer vanishes annihilated affine exposition conjecture update | non_dup | [] |
42698211 | 10.1007/s00029-017-0348-0 | We study graded nonlocal $\underline{\mathsf{q}}$-vertex algebras and we
prove that they can be generated by certain sets of vertex operators. As an
application, we consider the family of graded nonlocal
$\underline{\mathsf{q}}$-vertex algebras $V_{c,1}$, $c\geq 1$, associated with
the principal subspaces $W(c\Lambda_0)$ of the integrable highest weight $U_q
(\hat{\mathfrak{sl}}_2)$-modules $L(c\Lambda_0)$. Using quantum integrability,
we derive combinatorial bases for $V_{c,1}$ and compute the corresponding
character formulae.Comment: 28 pages, 1 figur | Higher level vertex operators for $U_q (\hat{\mathfrak{sl}}_2)$ | higher level vertex operators for $u_q (\hat{\mathfrak{sl}}_2)$ | graded nonlocal underline mathsf algebras operators. graded nonlocal underline mathsf algebras principal subspaces lambda integrable mathfrak modules lambda integrability derive combinatorial bases character pages figur | non_dup | [] |
111364709 | 10.1007/s00029-017-0349-z | In this paper we study higher Deligne–Lusztig representations of reductive\ud
groups over finite quotients of discrete valuation rings. At even levels, we show that\ud
these geometrically constructed representations, defined by Lusztig, coincide with\ud
certain explicit induced representations defined by Gérardin, thus giving a solution\ud
to a problem raised by Lusztig. In particular, we determine the dimensions of these\ud
representations. As an immediate application we verify a conjecture of Letellier for\ud
GL2 and GL3 | The algebraisation of higher Deligne–Lusztig representations. | the algebraisation of higher deligne–lusztig representations. | deligne–lusztig representations reductive quotients valuation rings. geometrically representations lusztig coincide representations gérardin giving raised lusztig. representations. immediate verify conjecture letellier | non_dup | [] |
73404603 | 10.1007/s00029-017-0381-z | Let k be a field of characteristic zero. Etingof and Kazhdan constructed a
quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice
of an associator Phi. They prove moreover that this quantisation is functorial
in b. Remarkably, the quantum group U_h(b) is endowed with a Tannakian
equivalence F_b from the braided tensor category of Drinfeld-Yetter modules
over b, with deformed associativity constraints given by Phi, to that of
Drinfeld-Yetter modules over U_h(b). In this paper, we prove that the
equivalence F_b is functorial in b.Comment: Small revisions in Sections 2 and 6. An appendix added on the
equivalence between admissible Drinfeld-Yetter modules over a QUE and modules
over its quantum double. To appear in Selecta Math. 71 page | A 2-categorical extension of Etingof-Kazhdan quantisation | a 2-categorical extension of etingof-kazhdan quantisation | zero. etingof kazhdan quantisation bialgebra associator phi. quantisation functorial remarkably endowed tannakian equivalence braided drinfeld yetter modules deformed associativity drinfeld yetter modules equivalence functorial revisions equivalence admissible drinfeld yetter modules modules double. selecta math. | non_dup | [] |
29499170 | 10.1007/s00029-017-0383-x | We present a theory of the $b$-function (or Bernstein-Sato polynomial) in
positive characteristic. Let $f$ be a non-constant polynomial with coefficients
in a perfect field $k$ of characteristic $p>0.$ Its $b$-function $b_f$ is
defined to be an ideal of the algebra of continuous $k$-valued functions on
$\mathbb{Z}_p.$ The zero-locus of the $b$-function is thus naturally
interpreted as a subset of $\mathbb{Z}_p,$ which we call the set of roots of
$b_f.$ We prove that $b_f$ has finitely many roots and that they are negative
rational numbers. Our construction builds on an earlier work of Musta\c{t}\u{a}
and is in terms of $D$-modules, where $D$ is the ring of Grothendieck
differential operators. We use the Frobenius to obtain finiteness properties of
$b_f$ and relate it to the test ideals of $f.$Comment: Final versio | On a theory of the $b$-function in positive characteristic | on a theory of the $b$-function in positive characteristic | bernstein sato characteristic. perfect ideal valued mathbb locus naturally interpreted mathbb call roots finitely roots rational numbers. builds musta modules grothendieck operators. frobenius finiteness relate ideals comment versio | non_dup | [] |
42641883 | 10.1007/s00029-017-0384-9 | We study the relative orbifold Donaldson-Thomas theory of
$[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$. We establish a
correspondence between the DT theory relative to 3 fibers to quantum
multiplication by divisors in the Hilbert scheme of points on
$[\mathbb{C}^2/\mathbb{Z}_{n+1}]$. This determines the whole theory if a
further nondegeneracy condition is assumed. The result can also be viewed as a
crepant resolution correspondence to the DT theory of $\mathcal{A}_n\times
\mathbb{P}^1$.Comment: 44 pages, 1 figure. Minor changes, Selecta Mathematica New Series
(2018 | Donaldson-Thomas theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times
\mathbb{P}^1$ | donaldson-thomas theory of $[\mathbb{c}^2/\mathbb{z}_{n+1}]\times \mathbb{p}^1$ | orbifold donaldson thomas mathbb mathbb mathbb establish correspondence fibers multiplication divisors hilbert mathbb mathbb determines nondegeneracy assumed. viewed crepant correspondence mathcal mathbb .comment pages figure. minor selecta mathematica | non_dup | [] |
73408994 | 10.1007/s00029-017-0387-6 | The Littlewood--Richardson process is a discrete random point process arising
from the isotypic decomposition of tensor products of irreducible
representations of $\operatorname{GL}_N(\mathbb{C})$. Biane--Perelomov--Popov
matrices are quantum random matrices obtained as the geometric quantization of
random Hermitian matrices with deterministic eigenvalues and uniformly random
eigenvectors. As first observed by Biane, correlation functions of certain
global observables of the LR process coincide with correlation functions of
linear statistics of sums of classically independent BPP matrices, thereby
enabling a random matrix approach to the statistical study of
$\operatorname{GL}_N(\mathbb{C})$ tensor products. In this paper, we prove an
optimal result: classically independent BPP matrices become freely independent
in any semiclassical/large-dimension limit. This proves and generalizes a
conjecture of Bufetov and Gorin, and leads to a Law of Large Numbers for the
BPP observables of the LR process which holds in any and all semiclassical
scalings.Comment: 52 page | Semiclassical asymptotics of $\operatorname{GL}_N(\mathbb{C})$ tensor
products and quantum random matrices | semiclassical asymptotics of $\operatorname{gl}_n(\mathbb{c})$ tensor products and quantum random matrices | littlewood richardson arising isotypic decomposition irreducible representations operatorname mathbb biane perelomov popov geometric quantization hermitian deterministic eigenvalues uniformly eigenvectors. biane observables coincide sums classically thereby enabling operatorname mathbb products. classically freely semiclassical limit. proves generalizes conjecture bufetov gorin observables semiclassical | non_dup | [] |
42668626 | 10.1007/s00029-018-0389-z | We study plane partitions satisfying condition $a_{n+1,m+1}=0$ (this
condition is called "pit") and asymptotic conditions along three coordinate
axes. We find the formulas for generating function of such plane partitions.
Such plane partitions label the basis vectors in certain representations of
quantum toroidal $\mathfrak{gl}_1$ algebra, therefore our formulas can be
interpreted as the characters of these representations. The resulting formulas
resemble formulas for characters of tensor representations of Lie superalgebra
$\mathfrak{gl}_{m|n}$. We discuss representation theoretic interpretation of
our formulas using $q$-deformed $W$-algebra $\mathfrak{gl}_{m|n}$.Comment: 30 pages, v2. 32 pages, new subsection 4.4 included, v3 36 pages,
many corrections, references added, v4 38 pages many corrections, references
added, version to appear in Sel. Math. New Ser. (2018 | Plane partitions with a "pit": generating functions and representation
theory | plane partitions with a "pit": generating functions and representation theory | partitions satisfying asymptotic coordinate axes. formulas generating partitions. partitions label representations toroidal mathfrak formulas interpreted characters representations. formulas resemble formulas characters representations superalgebra mathfrak theoretic formulas deformed mathfrak .comment pages pages subsection pages pages sel. math. ser. | non_dup | [] |
73956427 | 10.1007/s00029-018-0394-2 | Following the proof of the purity conjecture for weakly separated
collections, recent years have revealed a variety of wider examples of purity
in different settings. In this paper we consider the collection $\mathcal
A_{I,J}$ of sets that are weakly separated from two fixed sets $I$ and $J$. We
show that all maximal by inclusion weakly separated collections $\mathcal
W\subset\mathcal A_{I,J}$ are also maximal by size, provided that $I$ and $J$
are sufficiently "generic". We also give a simple formula for the cardinality
of $\mathcal W$ in terms of $I$ and $J$. We apply our result to calculate the
cluster distance and to give lower bounds on the mutation distance between
cluster variables in the cluster algebra structure on the coordinate ring of
the Grassmannian. Using a linear projection that relates weak separation to the
octahedron recurrence, we also find the exact mutation distances and cluster
distances for a family of cluster variables.Comment: 44 pages, 11 figure | Weak Separation, Pure Domains and Cluster Distance | weak separation, pure domains and cluster distance | purity conjecture weakly separated collections wider purity settings. mathcal weakly separated maximal inclusion weakly separated collections mathcal mathcal maximal sufficiently generic cardinality mathcal bounds mutation coordinate grassmannian. projection relates octahedron recurrence mutation distances distances pages | non_dup | [] |
73959871 | 10.1007/s00029-018-0405-3 | In this paper, we study the geometry of various Hessenberg varieties in type
A, as well as families thereof, with the additional goal of laying the
groundwork for future computations of Newton-Okounkov bodies of Hessenberg
varieties. Our main results are as follows. We find explicit and
computationally convenient generators for the local defining ideals of
indecomposable regular nilpotent Hessenberg varieties, and then show that all
regular nilpotent Hessenberg varieties are local complete intersections. We
also show that certain families of Hessenberg varieties, whose generic fibers
are regular semisimple Hessenberg varieties and the special fiber is a regular
nilpotent Hessenberg variety, are flat and have reduced fibres. This result
further allows us to give a computationally effective formula for the degree of
a regular nilpotent Hessenberg variety with respect to a Pl\"ucker embedding.
Furthermore, we construct certain flags of subvarieties of a regular nilpotent
Hessenberg variety, obtained by intersecting with Schubert varieties, which are
suitable for computing Newton-Okounkov bodies. As an application of our
results, we explicitly compute many Newton-Okounkov bodies of the
two-dimensional Peterson variety with respect to Pl\"ucker embeddings.Comment: 25 pages. Arguments substantially streamlined thanks to comments from
anonymous referee. Readers who want more leisurely explanations may wish to
consult our first version on the ArXi | Geometry of Hessenberg varieties with applications to Newton-Okounkov
bodies | geometry of hessenberg varieties with applications to newton-okounkov bodies | hessenberg varieties families thereof goal laying groundwork computations newton okounkov bodies hessenberg varieties. follows. computationally convenient generators defining ideals indecomposable nilpotent hessenberg varieties nilpotent hessenberg varieties intersections. families hessenberg varieties generic fibers semisimple hessenberg varieties fiber nilpotent hessenberg fibres. computationally nilpotent hessenberg ucker embedding. flags subvarieties nilpotent hessenberg intersecting schubert varieties newton okounkov bodies. explicitly newton okounkov bodies peterson ucker pages. arguments substantially streamlined thanks comments anonymous referee. readers want leisurely explanations wish consult arxi | non_dup | [] |
73350291 | 10.1007/s00029-018-0406-2 | We define and study coisotropic structures on morphisms of commutative dg
algebras in the context of shifted Poisson geometry, i.e. $P_n$-algebras.
Roughly speaking, a coisotropic morphism is given by a $P_{n+1}$-algebra acting
on a $P_n$-algebra. One of our main results is an identification of the space
of such coisotropic structures with the space of Maurer--Cartan elements in a
certain dg Lie algebra of relative polyvector fields. To achieve this goal, we
construct a cofibrant replacement of the operad controlling coisotropic
morphisms by analogy with the Swiss-cheese operad which can be of independent
interest. Finally, we show that morphisms of shifted Poisson algebras are
identified with coisotropic structures on their graph.Comment: 49 pages. v2: many proofs rewritten and the paper is split into two
part | Derived coisotropic structures I: affine case | derived coisotropic structures i: affine case | coisotropic morphisms commutative algebras shifted poisson i.e. algebras. roughly speaking coisotropic morphism acting algebra. coisotropic maurer cartan polyvector fields. goal cofibrant replacement operad controlling coisotropic morphisms analogy swiss cheese operad interest. morphisms shifted poisson algebras coisotropic pages. proofs rewritten split | non_dup | [] |
83848170 | 10.1007/s00029-018-0407-1 | We extend results about $n$-shifted coisotropic structures from part I of
this work to the setting of derived Artin stacks. We show that an intersection
of coisotropic morphisms carries a Poisson structure of shift one less. We also
compare non-degenerate shifted coisotropic structures and shifted Lagrangian
structures and show that there is a natural equivalence between the two spaces
in agreement with the classical result. Finally, we define quantizations of
$n$-shifted coisotropic structures and show that they exist for $n>1$.Comment: 45 pages. Contains the second half of arXiv:1608.01482v1 with new
material adde | Derived coisotropic structures II: stacks and quantization | derived coisotropic structures ii: stacks and quantization | extend shifted coisotropic artin stacks. intersection coisotropic morphisms carries poisson less. degenerate shifted coisotropic shifted lagrangian equivalence result. quantizations shifted coisotropic .comment pages. adde | non_dup | [] |
83831537 | 10.1007/s00029-018-0412-4 | We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's
geometric construction of crystal graphs from the symmetric to the
symmetrizable case. We also construct semicanonical functions in the
convolution algebras of generalized preprojective algebras. Conjecturally these
functions yield semicanonical bases of the enveloping algebras of the positive
part of symmetrizable Kac-Moody algebras.Comment: 50 pages. Version 2: A few typos fixed. Final version published in
Selecta Mathematic | Quivers with relations for symmetrizable Cartan matrices IV: Crystal
graphs and semicanonical functions | quivers with relations for symmetrizable cartan matrices iv: crystal graphs and semicanonical functions | generalize lusztig nilpotent varieties kashiwara saito geometric symmetrizable case. semicanonical convolution algebras preprojective algebras. conjecturally semicanonical bases enveloping algebras symmetrizable moody pages. typos fixed. selecta mathematic | non_dup | [] |
73384550 | 10.1007/s00029-018-0423-1 | The orbits of the orthogonal and symplectic groups on the flag variety are in
bijection, respectively, with the involutions and fixed-point-free involutions
in the symmetric group $S_n$. Wyser and Yong have described polynomial
representatives for the cohomology classes of the closures of these orbits,
which we denote as $\hat{\mathfrak{S}}_y$ (to be called involution Schubert
polynomials) and $\hat{\mathfrak{S}}^{\tt FPF}_y$ (to be called
fixed-point-free involution Schubert polynomials). Our main results are
explicit formulas decomposing the product of $\hat{\mathfrak{S}}_y$
(respectively, $\hat{\mathfrak{S}}^{\tt FPF}_y$) with any $y$-invariant linear
polynomial as a linear combination of other involution Schubert polynomials.
These identities serve as analogues of Lascoux and Sch\"utzenberger's
transition formula for Schubert polynomials, and lead to a self-contained
algebraic proof of the nontrivial equivalence of several definitions of
$\hat{\mathfrak{S}}_y$ and $\hat{\mathfrak{S}}^{\tt FPF}_y$ appearing in the
literature. Our formulas also imply combinatorial identities about involution
words, certain variations of reduced words for involutions in $S_n$. We
construct operators on involution words based on the Little map to prove these
identities bijectively. The proofs of our main theorems depend on some new
technical results, extending work of Incitti, about covering relations in the
Bruhat order of $S_n$ restricted to involutions.Comment: 31 pages; v2: updated references and acknowledgments; v3: added
references, minor corrections; v4: a few more references, examples, and
corrections, final versio | Transition formulas for involution Schubert polynomials | transition formulas for involution schubert polynomials | orbits orthogonal symplectic flag bijection involutions involutions wyser yong representatives cohomology closures orbits mathfrak involution schubert polynomials mathfrak involution schubert polynomials formulas decomposing mathfrak mathfrak involution schubert polynomials. identities serve analogues lascoux utzenberger schubert polynomials algebraic nontrivial equivalence definitions mathfrak mathfrak appearing literature. formulas imply combinatorial identities involution involutions involution identities bijectively. proofs theorems extending incitti covering bruhat restricted pages updated acknowledgments minor versio | non_dup | [] |
73372313 | 10.1007/s00029-018-0429-8 | We give an explicit description of the trace, or Hochschild homology, of the
quantum Heisenberg category defined by Licata and Savage. We also show that as
an algebra, it is isomorphic to "half" of a central extension of the elliptic
Hall algebra of Burban and Schiffmann, specialized at $\sigma = \bar\sigma^{-1}
= q$. A key step in the proof may be of independent interest: we show that the
sum (over $n$) of the Hochschild homologies of the positive affine Hecke
algebras $\mathrm{AH}_n^+$ is again an algebra, and that this algebra injects
into both the elliptic Hall algebra and the trace of the $q$-Heisenberg
category. Finally, we show that a natural action of the trace algebra on the
space of symmetric functions agrees with the specialization of an action
constructed by Schiffmann and Vasserot using Hilbert schemes.Comment: 49 pages, numerous figure | The Elliptic Hall algebra and the deformed Khovanov Heisenberg category | the elliptic hall algebra and the deformed khovanov heisenberg category | trace hochschild homology heisenberg licata savage. isomorphic elliptic hall burban schiffmann specialized sigma sigma hochschild homologies affine hecke algebras mathrm injects elliptic hall trace heisenberg category. trace agrees specialization schiffmann vasserot hilbert pages numerous | non_dup | [] |
93950215 | 10.1007/s00029-018-0434-y | A geometric approach to immersion formulas for soliton surfaces is provided
through new cohomologies on spaces of special types of $\mathfrak{g}$-valued
differential forms. This leads us to introduce Poincar\'e-type lemmas for these
cohomologies, which appropriately describe the integrability conditions of Lax
pairs associated with systems of PDEs. Our methods clarify the structure and
properties of the deformations and soliton surfaces for the aforesaid Lax
pairs. Our findings also allow for the generalization of the theory of soliton
surfaces in Lie algebras to general soliton submanifolds. Techniques from the
theory of infinite-dimensional jet manifolds and diffieties enable us to
justify certain common assumptions of the theory of soliton surfaces.
Theoretical results are illustrated through $\mathbb{C}P^{N-1}$ sigma models.Comment: 30 pages. Several typos corrected and some comments adde | A cohomological approach to immersed submanifolds via integrable systems | a cohomological approach to immersed submanifolds via integrable systems | geometric immersion formulas soliton cohomologies mathfrak valued forms. poincar lemmas cohomologies appropriately integrability pdes. clarify deformations soliton aforesaid pairs. generalization soliton algebras soliton submanifolds. infinite manifolds diffieties enable justify assumptions soliton surfaces. illustrated mathbb sigma pages. typos corrected comments adde | non_dup | [] |
73410536 | 10.1007/s00029-018-0435-x | We introduce a new link invariant called the algebraic genus, which gives an
upper bound for the topological slice genus of links. In fact, the algebraic
genus is an upper bound for another version of the slice genus proposed here:
the minimal genus of a surface in the four-ball whose complement has infinite
cyclic fundamental group. We characterize the algebraic genus in terms of
cobordisms in three-space, and explore the connections to other knot invariants
related to the Seifert form, the Blanchfield form, knot genera and unknotting.
Employing Casson-Gordon invariants, we discuss the algebraic genus as a
candidate for the optimal upper bound for the topological slice genus that is
determined by the S-equivalence class of Seifert matrices.Comment: 29 pages, 5 figures, comments welcome! V2: Improved exposition and
figures, added an example, implemented referee's recommendations. Accepted
for publication in Selecta Mathematic | On classical upper bounds for slice genera | on classical upper bounds for slice genera | algebraic genus topological slice genus links. algebraic genus slice genus genus ball complement infinite cyclic group. characterize algebraic genus cobordisms explore connections knot invariants seifert blanchfield knot genera unknotting. employing casson gordon invariants algebraic genus candidate topological slice genus equivalence seifert pages comments welcome exposition implemented referee recommendations. publication selecta mathematic | non_dup | [] |
2574315 | 10.1007/s00030-003-1051-8 | We study the Hamilton-Jacobi equation for undiscounted exit time control
problems with general nonnegative Lagrangians using the dynamic programming
approach. We prove theorems characterizing the value function as the unique
bounded-from-below viscosity solution of the Hamilton-Jacobi equation which is
null on the target. The result applies to problems with the property that all
trajectories satisfying a certain integral condition must stay in a bounded
set. We allow problems for which the Lagrangian is not uniformly bounded below
by positive constants, in which the hypotheses of the known uniqueness results
for Hamilton-Jacobi equations are not satisfied. We apply our theorems to
eikonal equations from geometric optics, shape-from-shading equations from
image processing, and variants of the Fuller Problem.Comment: 29 pages, 0 figures, accepted for publication in NoDEA Nonlinear
Differential Equations and Applications on July 29, 200 | Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal
Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations,
and Shape-From-Shading | bounded-from-below solutions of the hamilton-jacobi equation for optimal control problems with exit times: vanishing lagrangians, eikonal equations, and shape-from-shading | hamilton jacobi undiscounted exit nonnegative lagrangians programming approach. theorems characterizing viscosity hamilton jacobi target. applies trajectories satisfying stay set. lagrangian uniformly hypotheses uniqueness hamilton jacobi satisfied. theorems eikonal geometric optics shading variants fuller pages publication nodea | non_dup | [] |
29513144 | 10.1007/s00030-007-2047-6 | In this paper, we consider a time independent $C^2$ Hamiltonian, sa\-tisfying
the usual hypothesis of the classical Calculus of Variations, on a non-compact
connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the
existence of weak KAM solutions, or viscosity solutions, for the associated
Hamilton-Jacobi Equation. This proof works also in presence of symmetries. We
also study the role of the amenability of the group of symmetries to understand
when the several critical values that can be associated with the Hamiltonian
coincide.Comment: arXiv admin note: text overlap with arXiv:1004.0086 by other author | Weak KAM theorem on non compact manifolds | weak kam theorem on non compact manifolds | tisfying usual calculus manifold. oleinik semigroup viscosity hamilton jacobi equation. symmetries. amenability symmetries admin overlap | non_dup | [] |
36728444 | 10.1007/s00030-009-0023-z | The article of record as published may be located at http://dx.doi.org/10.1007/s00030-009-0023-zIn this work, we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for solutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell-Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc | Large deviations for the stochastic shell model of turbulence | large deviations for the stochastic shell model of turbulence | record uniqueness stochastic turbulence multiplicative noise. laplace stochastic polish space. wentzell freidlin utilizing varadhan bryc | non_dup | [] |
2811769 | 10.1007/s00030-011-0105-6 | Countable families of global-in-time and blow-up similarity sign-changing patterns of the Cauchy problem for the fourth-order thin film equation (TFE-4) ut= -del . (|u|(n)del Delta u) in R(N) x R(+), where n > 0, are studied. The similarity solutions are of standard "forward" and "backward" forms u(+/-)(x, t) = (+/- t)(-alpha)f(y), y = x/(+/- t)(beta), beta = 1-alpha n/4, +/- t>0, where f solve Bn+(alpha, f)equivalent to-del.(|f|n del Delta f)+/-beta y.del f +/-alpha f = 0 in RN, (0.1) and alpha is an element of R is a parameter (a "nonlinear eigenvalue"). The sign "+", i.e.,t > 0, corresponds to global asymptotics as t -> +infinity, while "-" (t < 0) yields blow-up limits t -> 0(-) describing possible "micro-scale" (multiple zero) structures of solutions of the PDE. To get a countable set of nonlinear pairs {f(gamma), alpha(gamma)}, a bifurcation-branching analysis is performed by using a homotopy path n -> 0(+) in (0.1), where B(0)(+/-) (alpha, f) become associated with a pair {B, B*} of linear non-self-adjoint operators B=-Delta(2) + 1/4 y.del+N/4 I and B*=-Delta(2) - 1/4y.( so (B)*(L2) = B*), which are known to possess a discrete real spectrum, sigma(B) = sigma(B*) = {lambda(gamma) = - |gamma/4|}(|gamma|>0) (gamma is a multiindex in R(N)). These operators occur after corresponding global and blow-up scaling of the classic bi-harmonic equation u(t) = -Delta(2)u. This allows us to trace out the origin of a countable family of n-branches of nonlinear eigenfunctions by using simple or semi-simple eigenvalues of the linear operators {B, B*} leading to important properties of oscillatory sign-changing nonlinear patterns of the TFE, at least, for small n > 0 | Local bifurcation-branching analysis of global and "blow-up" patterns for a fourth-order thin film equation | local bifurcation-branching analysis of global and "blow-up" patterns for a fourth-order thin film equation | countable families blow similarity changing cauchy fourth film delta studied. similarity backward alpha beta beta alpha solve alpha del. delta beta alpha alpha eigenvalue i.e. asymptotics infinity blow describing micro pde. countable gamma alpha gamma bifurcation branching homotopy alpha adjoint delta delta possess sigma sigma lambda gamma gamma gamma gamma multiindex blow classic harmonic delta trace countable branches eigenfunctions eigenvalues oscillatory changing | non_dup | [] |
2116386 | 10.1007/s00030-011-0107-4 | A simple version of exact finite dimensional reduction for the variational
setting of mechanical systems is presented. It is worked out by means of a
thorough global version of the implicit function theorem for monotone
operators. Moreover, the Hessian of the reduced function preserves all the
relevant information of the original one, by Schur's complement, which
spontaneously appears in this context. Finally, the results are
straightforwardly extended to the case of a Dirichlet problem on a bounded
domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential
Equations and Application | Finite reduction and Morse index estimates for mechanical systems | finite reduction and morse index estimates for mechanical systems | variational presented. worked thorough implicit monotone operators. hessian preserves schur complement spontaneously context. straightforwardly dirichlet pages minor | non_dup | [] |
54039251 | 10.1007/s00030-011-0148-8 | International audienceWe study the Cauchy-Dirichlet problem for the elliptic-parabolic equation $$b(u)_t +\div F(u) - \Delta u=f$$ in a bounded domain. We do not assume the structure condition ''$b(z)=b(\hat z) \Rightarrow F(z)=F(\hat z)$''. Our main goal is to investigate the problem of continuous dependence of the solutions on the data of the problem and the question of convergence of discretization methods. As in the work of Ammar and Wittbold \cite{AmmarWittbold} where existence was established, monotonicity and penalization are the main tools of our study. In the case of a Lipschitz continuous flux $F$, we justify the uniqueness of $u$ (the uniqueness of $b(u)$ is well-known) and prove the continuous dependence in $L^1$ for the case of strongly convergent finite energy data. We also prove convergence of the $\varepsilon$-discretized solutions used in the semigroup approach to the problem; and we prove convergence of a monotone time-implicit finite volume scheme. In the case of a merely continuous flux $F$, we show that the problem admits a maximal and a minimal solution | Convergence of approximate solutions to an elliptic-parabolic equation without the structure condition | convergence of approximate solutions to an elliptic-parabolic equation without the structure condition | audiencewe cauchy dirichlet elliptic parabolic delta domain. rightarrow goal discretization methods. ammar wittbold cite ammarwittbold monotonicity penalization study. lipschitz justify uniqueness uniqueness convergent data. varepsilon discretized semigroup monotone implicit scheme. merely admits maximal | non_dup | [] |
47104741 | 10.1007/s00030-012-0155-4 | 26 pagesInternational audienceThe hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An adaptation of the notion of duality solutions, introduced for linear equations with discontinuous coefficients, leads to an existence result. Uniqueness is obtained through a precise definition of the nonlinear flux as well as the complete dynamics of aggregates, i.e. combinations of Dirac masses. Finally a particle method is used to build an adapted numerical scheme | Chemotaxis: from kinetic equations to aggregate dynamics | chemotaxis: from kinetic equations to aggregate dynamics | pagesinternational audiencethe hydrodynamic chemotaxis investigated. conservation blow giving valued discontinuous velocities. adaptation notion duality discontinuous result. uniqueness precise aggregates i.e. combinations dirac masses. build adapted | non_dup | [] |
52905238 | 10.1007/s00030-012-0156-3 | International audienceWe consider the asymptotic behavior of an evolving weakly coupled Fokker-Planck system of two equations set in a periodic environment. The magnitudes of the diffusion and the coupling are respectively proportional and inversely proportional to the size of the period. We prove that, as the period tends to zero, the solutions of the system either propagate (concentrate) with a fixed constant velocity (determined by the data) or do not move at all. The system arises in the modeling of motor proteins which can take two different states. Our result implies that, in the limit, the molecules either move along a filament with a fixed direction and constant speed or remain immobile | A homogenization approach for the motion of motor proteins | a homogenization approach for the motion of motor proteins | audiencewe asymptotic evolving weakly fokker planck environment. magnitudes inversely period. tends propagate concentrate move all. arises motor states. move filament immobile | non_dup | [] |
55621257 | 10.1007/s00030-012-0204-z | For the initial value problem (IVP) associated to the generalized
Korteweg-de Vries (gKdV) equation with supercritical nonlinearity,
\begin{equation*}
u_{t}+\partial_x^3u+\partial_x(u^{k+1}) =0,\qquad k\geq 5,
\end{equation*}
numerical evidence [Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R.: Conservative, high-order numerical schemes for the generalized Korteweg–de Vries equation. Philos. Trans. Roy. Soc. London Ser. A 351, 107–164 (1995) ] shows that, there are initial data $\phi\in
H^1(\mathbb{R})$ such that the corresponding solution may blow-up in finite time.
Also, with the evidence from numerical simulation [Abdullaev F.K., Caputo J.G., Kraenkel R.A., Malomed B.A.: Controlling collapse in Bose–Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A 67, 012605 (2003) and Konotop V.V., Pacciani P.: Collapse of solutions of the nonlinear Schrödinger equation with a time dependent nonlinearity: application to the Bose–Einstein condensates. Phys. Rev. Lett. 94, 240405 (2005) ], it has been
claimed that a periodic time dependent coefficient in the nonlinearity would disturb the
blow-up solution, either accelerating or delaying it.
In this work, we investigate the IVP associated to the gKdV equation
\begin{equation*}
u_{t}+\partial_x^3u+g(\omega t)\partial_x(u^{k+1}) =0,
\end{equation*}
where $g$ is a periodic function and $k\geq 5$ is an integer. We prove that, for given
initial data $\phi \in H^1(\mathbb{R})$, as $|\omega|\to \infty$, the solution $u_{\omega}$
converges to the solution $U$ of the initial value problem associated to
\begin{equation*}
U_{t}+\partial_x^3U+m(g)\partial_x(U^{k+1}) =0,
\end{equation*}
with the same initial data, where $m(g)$ is the average of the periodic function $g$.
Moreover, if the solution $U$ is global and satisfies $\|U\|_{L_x^5L_t^{10}}<\infty$, then
we prove that the solution $u_{\omega}$ is also global provided $|\omega|$ is
sufficiently large.M. P. was partially supported by the Research Center of Mathematics of the University of Minho, Portugal through the FCT Pluriannual Funding Program, and through the project PTDC/MAT/109844/2009, and M. S. was partially supported by FAPESP Brazil | On the supercritical KDV equation with time-oscillating nonlinearity | on the supercritical kdv equation with time-oscillating nonlinearity | korteweg vries gkdv supercritical nonlinearity begin qquad bona j.l. dougalis v.a. karakashian o.a. mckinney w.r. conservative schemes korteweg–de vries equation. philos. trans. roy. soc. ser. mathbb blow time. abdullaev f.k. caputo j.g. kraenkel r.a. malomed b.a. controlling collapse bose–einstein condensates modulation length. phys. rev. konotop v.v. pacciani collapse schrödinger nonlinearity bose–einstein condensates. phys. rev. lett. claimed nonlinearity disturb blow accelerating delaying gkdv begin omega integer. mathbb omega infty omega converges begin satisfies infty omega omega sufficiently large.m. partially mathematics minho portugal pluriannual funding ptdc partially fapesp brazil | non_dup | [] |
5236932 | 10.1007/s00030-013-0220-7 | We study the long time behavior of solutions of the Cauchy problem for
nonlinear reaction-diffusion equations in one space dimension with the
nonlinearity of bistable, ignition or monostable type. We prove a one-to-one
relation between the long time behavior of the solution and the limit value of
its energy for symmetric decreasing initial data in $L^2$ under minimal
assumptions on the nonlinearities. The obtained relation allows to establish
sharp threshold results between propagation and extinction for monotone
families of initial data in the considered general setting | Threshold phenomena for symmetric decreasing solutions of
reaction-diffusion equations | threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations | cauchy nonlinearity bistable ignition monostable type. decreasing assumptions nonlinearities. establish sharp propagation extinction monotone families | non_dup | [] |
9706634 | 10.1007/s00030-013-0223-4 | We modify the approach of Burton and Toland Comm. Pure Appl. Math. (2011) to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period | On the stability of travelling waves with vorticity obtained by minimization | on the stability of travelling waves with vorticity obtained by minimization | modify burton toland comm. appl. math. vorticity suited analysis. enlarging stream necessarily travelling profiles. stream priori vanish galilean coordinate system. travelling minimisation preserved evolutionary minimisation burton toland maximisation circulation impulse becoming lagrange multiplier preclude flows choosing appropriately vorticity. conditional energetic minimizers perturbations spatially | non_dup | [] |
24941634 | 10.1007/s00030-013-0258-6 | In this article, we study the Fu\v{c}ik spectrum of fractional Laplace
operator which is defined as the set of all $(\al,\ba)\in \mb
R^2$ such that
\begin{equation*}
\quad \left. \begin{array}{lr}
\quad (-\De)^s u = \al u^{+} - \ba u^{-} \; \text{in}\; \Om
\quad \quad \quad \quad u = 0 \; \mbox{in}\; \mb R^n \setminus\Om.\\
\end{array} \quad \right\} \end{equation*} has a non-trivial solution $u$,
where $\Om$ is a bounded domain in $\mb R^n$ with Lipschitz boundary, $n>2s$,
$s\in(0,1)$. The existence of a first nontrivial curve $\mc C$ of this
spectrum, some properties of this curve $\mc C$, e.g. Lipschitz continuous,
strictly decreasing and asymptotic behavior are studied in this article. A
variational characterization of second eigenvalue of the fractional eigenvalue
problem is also obtained. At the end, we study a nonresonance problem with
respect to Fu\v{c}ik spectrum.Comment: 22 pages in NoDEA: Nonlinear differential equations and applications,
201 | On The Fu\v{c}ik Spectrum Of Non-Local Elliptic Operators | on the fu\v{c}ik spectrum of non-local elliptic operators | fractional laplace begin quad left. begin array quad quad quad quad quad mbox setminus array quad trivial lipschitz nontrivial e.g. lipschitz strictly decreasing asymptotic article. variational eigenvalue fractional eigenvalue obtained. nonresonance pages nodea | non_dup | [] |
24989724 | 10.1007/s00030-014-0266-1 | We consider the non-linear thermoelastic plate equation in rectangular
domains $\Omega$. More precisely, $\Omega$ is considered to be given as the
Cartesian product of whole or half spaces and a cube. First the linearized
equation is treated as an abstract Cauchy problem in $L^p$-spaces. We take
advantage of the structure of $\Omega$ and apply operator-valued Fourier
multiplier results to infer an $\mathcal R$-bounded $\mathcal
H^\infty$-calculus. With the help of maximal $L^p$-regularity existence and
uniqueness of local real-analytic strong solutions together with analytic
dependency on the data is shown.Comment: 16 pages; final versio | Local Strong Solutions for the Non-Linear Thermoelastic Plate Equation
on Rectangular Domains in $L^p$-Spaces | local strong solutions for the non-linear thermoelastic plate equation on rectangular domains in $l^p$-spaces | thermoelastic plate rectangular omega precisely omega cartesian cube. linearized cauchy spaces. advantage omega valued fourier multiplier infer mathcal mathcal infty calculus. maximal regularity uniqueness analytic analytic dependency pages versio | non_dup | [] |
54007894 | 10.1007/s00030-014-0267-0 | We study the controllability for a class of semilinear differential inclusions in Banach spaces. Since we assume the regularity of the nonlinear part with respect to the weak topology, we do not require the compactness of the evolution operator generated by the linear part. As well we are not posing any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. We are considering the usual assumption on the controllability of the associated linear problem. Notice that, in infinite dimensional spaces, the above mentioned compactness of\ud
the evolution operator and linear controllability condition are in contradiction with each other. We suppose that the nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. This regularity setting allows us to solve controllability problem under various growth conditions. As application, a controllability result for hyperbolic integro-differential equations and inclusions is obtained. In particular, we consider controllability of a system arising in a model of nonlocal spatial population dispersal and a system governed by the second order one-dimensional telegraph equation | Controllability for systems governed by semilinear evolution equations without compactness | controllability for systems governed by semilinear evolution equations without compactness | controllability semilinear inclusions banach spaces. regularity topology compactness part. posing multivalued nonlinearity noncompactness. usual controllability problem. notice infinite compactness controllability contradiction other. convex weakly sequentially restricted argument. regularity solve controllability conditions. controllability hyperbolic integro inclusions obtained. controllability arising nonlocal dispersal governed telegraph | non_dup | [] |
25047559 | 10.1007/s00030-015-0311-8 | We provide new results on the existence, non-existence, localization and
multiplicity of nontrivial solutions for systems of Hammerstein integral
equations. Some of the criteria involve a comparison with the spectral radii of
some associated linear operators. We apply our results to prove the existence
of multiple nonzero radial solutions for some systems of elliptic boundary
value problems subject to nonlocal boundary conditions. Our approach is
topological and relies on the classical fixed point index. We present an
example to illustrate our theory.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1404.139 | Nonzero radial solutions for a class of elliptic systems with nonlocal
BCs on annular domains | nonzero radial solutions for a class of elliptic systems with nonlocal bcs on annular domains | localization multiplicity nontrivial hammerstein equations. involve radii operators. nonzero elliptic nonlocal conditions. topological relies index. illustrate pages. admin overlap | non_dup | [] |
29504570 | 10.1007/s00030-015-0315-4 | We study the existence of positive viscosity solutions to Trudinger's
equation for cylindrical domains $\Omega\times[0, T)$, where $\Omega\subset
\mathbb{R}^n,\;n\ge 2,$ is a bounded domain, $T>0$ and $2\leq p<\infty$. We
show existence for general domains $\Omega,$ when $n<p<\infty$. For $2\leq
p\leq n$, we prove existence for domains $\Omega$ that satisfy a uniform outer
ball condition. We achieve this by constructing suitable sub-solutions and
super-solutions and applying Perron's method.Comment: 25 pages, 2 figure | On the viscosity solutions to Trudinger's equation | on the viscosity solutions to trudinger's equation | viscosity trudinger cylindrical omega omega mathbb infty omega infty omega satisfy outer ball condition. constructing super perron pages | non_dup | [] |
25047368 | 10.1007/s00030-015-0341-2 | We study the propagation of singularities for semilinear Schrodinger
equations with quadratic Hamiltonians, in particular for the semilinear
harmonic oscillator. We show that the propagation still occurs along the flow
the Hamiltonian flow, but for Sobolev regularities in a certain range and
provided the notion of Sobolev-wave front set is conveniently modified. The
proof makes use of a weighted version of the paradifferential calculus, adapted
to our situation. The results can be regarded as the Schrodinger counterpart of
those known for semilinear hyperbolic equations, which hold with the usual wave
front set.Comment: 16 page | Propagation of singularities for semilinear Schr\"odinger equations | propagation of singularities for semilinear schr\"odinger equations | propagation singularities semilinear schrodinger quadratic hamiltonians semilinear harmonic oscillator. propagation sobolev regularities notion sobolev front conveniently modified. weighted paradifferential calculus adapted situation. regarded schrodinger counterpart semilinear hyperbolic hold usual front | non_dup | [] |
29556415 | 10.1007/s00030-015-0350-1 | We generalize the notion of renormalized solution to semilinear elliptic and
parabolic equations involving operator associated with general (possibly
nonlocal) regular Dirichlet form and smooth measure on the right-hand side. We
show that under mild integrability assumption on the data a quasi-continuous
function $u$ is a renormalized solution to an elliptic (or parabolic) equation
in the sense of our definition iff $u$ is its probabilistic solution, i.e. $u$
can be represented by a suitable nonlinear Feynman-Kac formula. This implies in
particular that for a broad class of local and nonlocal semilinear equations
there exists a unique renormalized solution | Renormalized solutions of semilinear equations involving measure data
and operator corresponding to Dirichlet form | renormalized solutions of semilinear equations involving measure data and operator corresponding to dirichlet form | generalize notion renormalized semilinear elliptic parabolic involving possibly nonlocal dirichlet side. mild integrability quasi renormalized elliptic parabolic probabilistic i.e. feynman formula. broad nonlocal semilinear renormalized | non_dup | [] |
48159764 | 10.1007/s00030-016-0401-2 | article 47International audienceWe study existence and uniqueness of the invariant measure for a stochastic process with degenerate diffusion, whose infinitesimal generator is a linear subelliptic operator in the whole space R N with coefficients that may be unbounded. Such a measure together with a Liouville-type theorem will play a crucial role in two applications: the ergodic problem studied through stationary problems with vanishing discount and the long time behavior of the solution to a parabolic Cauchy problem. In both cases, the constants will be characterized in terms of the invariant measure | The ergodic problem for some subelliptic operators with unbounded coefficients | the ergodic problem for some subelliptic operators with unbounded coefficients | audiencewe uniqueness stochastic degenerate infinitesimal generator subelliptic unbounded. liouville crucial ergodic stationary vanishing discount parabolic cauchy problem. | non_dup | [] |
42706979 | 10.1007/s00030-016-0408-8 | We study the Cauchy problem for a nonlinear damped wave equation. Under
suitable assumptions for the nonlinearity and the initial data, we obtain the
global solution which satisfies weighted $L^1$ and $L^\infty$ estimates.
Furthermore, we establish the higher order asymptotic expansion of the
solution. This means that we construct the nonlinear approximation of the
global solution with respect to the weight of the data. Our proof is based on
the approximation formula of the linear solution, which is given in [36], and
the nonlinear approximation theory for a nonlinear parabolic equation developed
by [18] | Higher order asymptotic expansions to the solutions for a nonlinear
damped wave equation | higher order asymptotic expansions to the solutions for a nonlinear damped wave equation | cauchy damped equation. assumptions nonlinearity satisfies weighted infty estimates. establish asymptotic solution. data. parabolic | non_dup | [] |
29540736 | 10.1007/s00030-016-0411-0 | We prove existence and multiplicity results for finite energy solutions to
the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right)
u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq
\mathbb{R}^{N},\ N\geq 3, \] where $\Omega $ is a radial domain (bounded or
unbounded) and $u$ satisfies $u=0$ on $\partial \Omega $ if $\Omega \neq
\mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty $
if $\Omega $ is unbounded. The potential $V$ may be vanishing or unbounded at
zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear.
If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq
0$ is also considered.Comment: 29 pages, 8 figure | Compactness and existence results in weighted Sobolev spaces of radial
functions. Part II: Existence | compactness and existence results in weighted sobolev spaces of radial functions. part ii: existence | multiplicity elliptic triangle quad textrm omega subseteq mathbb omega unbounded satisfies omega omega mathbb rightarrow rightarrow infty omega unbounded. vanishing unbounded infinity nonlinearity superlinear sublinear. sublinear cdot pages | non_dup | [] |
42745274 | 10.1007/s00030-016-0424-8 | We consider the nonlinear Choquard equation $$ -\Delta u+V u=(I_\alpha \ast
\vert u\vert ^p)\vert u\vert ^{p-2}u \qquad \text{ in } \mathbb{R}^N $$ where
$N\geq 1$, $I_\alpha$ is the Riesz potential integral operator of order $\alpha
\in (0, N)$ and $p > 1$. If the potential $ V \in C (\mathbb{R}^N; [0,+\infty))
$ satisfies the confining condition $$ \liminf\limits_{\vert x\vert \to
+\infty}\frac{V(x)}{1+\vert x\vert ^{\frac{N+\alpha}{p}-N}}=+\infty, $$ and
$\frac{1}{p} > \frac{N - 2}{N + \alpha}$, we show the existence of a
groundstate, of an infinite sequence of solutions of unbounded energy and, when
$p \ge 2$ the existence of least energy nodal solution. The constructions are
based on suitable weighted compact embedding theorems. The growth assumption is
sharp in view of a Poho\v{z}aev identity that we establish.Comment: 21 page | Choquard equations under confining external potentials | choquard equations under confining external potentials | choquard delta alpha vert vert vert vert qquad mathbb alpha riesz alpha mathbb infty satisfies confining liminf vert vert infty frac vert vert frac alpha infty frac frac alpha groundstate infinite unbounded nodal solution. constructions weighted embedding theorems. sharp poho | non_dup | [] |
42724468 | 10.1007/s00030-017-0434-1 | We study the Cauchy problem for the nonlinear damped wave equation and
establish the large data local well-posedness and small data global
well-posedness with slowly decaying initial data. We also prove that the
asymptotic profile of the global solution is given by a solution of the
corresponding parabolic problem, which shows that the solution of the damped
wave equation has the diffusion phenomena. Moreover, we show blow-up of
solution and give the estimate of the lifespan for a subcritical nonlinearity.
In particular, we determine the critical exponent for any space dimension.Comment: 43 pages. Theorem 1.3 is improved, some errors are corrected and
references are update | The Cauchy problem for the nonlinear damped wave equation with slowly
decaying data | the cauchy problem for the nonlinear damped wave equation with slowly decaying data | cauchy damped establish posedness posedness slowly decaying data. asymptotic parabolic damped phenomena. blow lifespan subcritical nonlinearity. exponent pages. corrected update | non_dup | [] |
29506022 | 10.1007/s00030-017-0436-z | This paper concerns integral varifolds of arbitrary dimension in an open
subset of Euclidean space satisfying integrability conditions on their first
variation. Firstly, the study of pointwise power decay rates almost everywhere
of the quadratic tilt-excess is completed by establishing the precise decay
rate for two-dimensional integral varifolds of locally bounded first variation.
In order to obtain the exact decay rate, a coercive estimate involving a
height-excess quantity measured in Orlicz spaces is established. Moreover,
counter-examples to pointwise power decay rates almost everywhere of the
super-quadratic tilt-excess are obtained. These examples are optimal in terms
of the dimension of the varifold and the exponent of the integrability
condition in most cases, for example if the varifold is not two-dimensional.
These examples also demonstrate that within the scale of Lebesgue spaces no
local higher integrability of the second fundamental form, of an at least
two-dimensional curvature varifold, may be deduced from boundedness of its
generalised mean curvature vector.
Amongst the tools are Cartesian products of curvature varifolds.Comment: mainly extended the overview section; updated reference | Decay rates for the quadratic and super-quadratic tilt-excess of
integral varifolds | decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds | concerns varifolds euclidean satisfying integrability variation. firstly pointwise everywhere quadratic tilt excess completed establishing precise varifolds locally variation. coercive involving excess quantity orlicz established. counter pointwise everywhere super quadratic tilt excess obtained. varifold exponent integrability varifold dimensional. lebesgue integrability curvature varifold deduced boundedness generalised curvature vector. amongst cartesian curvature overview updated | non_dup | [] |
42663733 | 10.1007/s00030-017-0457-7 | We study the mean curvature flow of graphs both with Neumann boundary
conditions and transport terms. We derive boundary gradient estimates for the
mean curvature flow. As an application, the existence of the mean curvature
flow of graphs is presented. A key argument is a boundary monotonicity formula
of a Huisken type derived using reflected backward heat kernels. Furthermore,
we provide regularity conditions for the transport terms.Comment: 21 pages, 3 figures, Accepted for publication in "NoDEA. Nonlinear
Differential Equations and Applications | Gradient estimates for mean curvature flow with Neumann boundary
conditions | gradient estimates for mean curvature flow with neumann boundary conditions | curvature neumann terms. derive curvature flow. curvature presented. argument monotonicity huisken reflected backward kernels. regularity pages publication nodea. | non_dup | [] |
73957174 | 10.1007/s00030-017-0468-4 | The purpose of this paper is to investigate the time behavior of the solution
of a weighted $p$-Laplacian evolution equation, given by \begin{align}
\label{eveq} \begin{cases} u_{t} = \text{div} \left(\gamma |\nabla
u|^{p-2}\nabla u \right) & \text{on} (0,\infty)\times S, \\ \gamma|\nabla
u|^{p-2}\nabla u\cdot\eta=0 & \text{on} (0,\infty)\times \partial S, \\
u(0,\cdot)=u_{0} & \text{on} S,\end{cases} \end{align} where $n \in
\mathbb{N}\setminus \{1\}$, $p \in (1,\infty)\setminus \{2\}$, $S\subseteq
\mathbb{R}^{n}$ is an open, bounded and connected set of class $C^{1}$, $\eta$
is the unit outer normal on $\partial S $, and $\gamma: S \rightarrow
(0,\infty)$ is a bounded function which can be extended to an
$A_{p}$-Muckenhoupt weight on $\mathbb{R}^{n}$. It will be proven that the
solution converges in $L^{1}(S)$ to the average of the initial value $u_{0} \in
L^{1}(S)$. Moreover, a conservation of mass principle, an extinction principle
and a decay rate for the solution will be derived.Comment: The final paper is published in NoDEA (August 2017 - Volume 24 Issue
4) at http://link.springer.co | Asymptotic Results for Solutions of a weighted p-Laplacian evolution
Equation with Neumann Boundary Conditions | asymptotic results for solutions of a weighted p-laplacian evolution equation with neumann boundary conditions | weighted laplacian begin align label eveq begin gamma nabla nabla infty gamma nabla nabla cdot infty cdot align mathbb setminus infty setminus subseteq mathbb outer gamma rightarrow infty muckenhoupt mathbb proven converges conservation extinction nodea august link.springer.co | non_dup | [] |
42668583 | 10.1007/s00030-017-0477-3 | We introduce a class of stochastic Allen-Cahn equations with a mobility
coefficient and colored noise. For initial data with finite free energy, we
analyze the corresponding Cauchy problem on the $d$-dimensional torus in the
time interval $[0,T]$. Assuming that $d\le 3$ and that the potential has
quartic growth, we prove existence and uniqueness of the solution as a process
$u$ in $L^2$ with continuous paths, satisfying almost surely the regularity
properties $u\in C([0,T]; H^1)$ and $u\in L^2([0,T];H^2)$.Comment: 34 page | Stochastic Allen-Cahn equation with mobility | stochastic allen-cahn equation with mobility | stochastic allen cahn mobility colored noise. analyze cauchy torus quartic uniqueness paths satisfying surely regularity .comment | non_dup | [] |
42728478 | 10.1007/s00030-017-0487-1 | In this article, we study the Brezis-Nirenberg type problem of nonlinear
Choquard equation involving a fractional Laplacian \[ (-\De)^s u = \left(
\int_{\Om}\frac{|u|^{2^*_{\mu,s}}}{|x-y|^{\mu}}\mathrm{d}y
\right)|u|^{2^*_{\mu,s}-2}u +\la u \; \text{in } \Om,\] where $\Om $ is a
bounded domain in $\mathbb R^n$ with Lipschitz boundary, $\la $ is a real
parameter, $s \in (0,1)$, $n >2s$ and $2^*_{\mu,s}= (2n-\mu)/(n-2s)$ is the
critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We
obtain some existence, multiplicity, regularity and nonexistence results for
solution of the above equation using variational methods.Comment: 32 pages. arXiv admin note: text overlap with arXiv:1604.00826 by
other author | Fractional Choquard Equation with Critical Nonlinearities | fractional choquard equation with critical nonlinearities | brezis nirenberg choquard involving fractional laplacian frac mathrm mathbb lipschitz exponent hardy littlewood sobolev inequality. multiplicity regularity nonexistence variational pages. admin overlap | non_dup | [] |
42740271 | 10.1007/s00030-018-0500-3 | We show that the characterization of existence and uniqueness up to vertical
translations of solutions to the prescribed mean curvature equation, originally
proved by Giusti in the smooth case, holds true for domains satisfying very
mild regularity assumptions. Our results apply in particular to the
non-parametric solutions of the capillary problem for perfectly wetting fluids
in zero gravity. Among the essential tools used in the proofs, we mention a
\textit{generalized Gauss-Green theorem} based on the construction of the weak
normal trace of a vector field with bounded divergence, in the spirit of
classical results due to Anzellotti, and a \textit{weak Young's law} for
$(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector
fields have been now extended and moved in a self-contained paper available
at: arXiv:1708.0139 | The prescribed mean curvature equation in weakly regular domains | the prescribed mean curvature equation in weakly regular domains | uniqueness translations prescribed curvature originally proved giusti satisfying mild regularity assumptions. parametric capillary perfectly wetting fluids gravity. proofs mention textit gauss trace divergence spirit anzellotti textit lambda minimizers pages trace moved | non_dup | [] |
129348271 | 10.1007/s00030-018-0504-z | This paper considers a pair of coupled nonlinear Helmholtz equations
\begin{align*}
-\Delta u - \mu u = a(x) \left( |u|^\frac{p}{2} + b(x) |v|^\frac{p}{2}
\right)|u|^{\frac{p}{2} - 2}u, \end{align*} \begin{align*}
-\Delta v - \nu v = a(x) \left( |v|^\frac{p}{2} + b(x) |u|^\frac{p}{2}
\right)|v|^{\frac{p}{2} - 2}v \end{align*} on $\mathbb{R}^N$ where
$\frac{2(N+1)}{N-1} < p < 2^\ast$. The existence of nontrivial strong solutions
in $W^{2, p}(\mathbb{R}^N)$ is established using dual variational methods.
The focus lies on necessary and sufficient conditions on the parameters
deciding whether or not both components of such solutions are nontrivial.Comment: Published version. Contains minor revisions: Quote added,
explanations on p.12 concerning F_{\mu\nu} = \infty, correction of exponent
on p.1 | Dual Variational Methods for a nonlinear Helmholtz system | dual variational methods for a nonlinear helmholtz system | considers helmholtz begin align delta frac frac frac align begin align delta frac frac frac align mathbb frac nontrivial mathbb variational methods. lies deciding version. minor revisions quote explanations concerning infty exponent | non_dup | [] |
2560500 | 10.1007/s00031-004-7010-6 | Let $X$ be a smooth projective curve over the complex numbers. To every
representation $\rho\colon \GL(r)\lra \GL(V)$ of the complex general linear
group on the finite dimensional complex vector space $V$ which satisfies the
assumption that there be an integer $\alpha$ with $\rho(z \id_{\C^r})=z^\alpha
\id_V$ for all $z\in\C^*$ we associate the problem of classifying triples
$(E,L,\phi)$ where $E$ is a vector bundle of rank $r$ on $X$, $L$ is a line
bundle on $X$, and $\phi\colon E_\rho\lra L$ is a non trivial homomorphism.
Here, $E_\rho$ is the vector bundle of rank $\dim V$ associated to $E$ via
$\rho$. If we take, for example, the standard representation of $\GL(r)$ on
$\C^r$ we have to classify triples $(E,L,\phi)$ consisting of $E$ as before and
a non-zero homomorphism $\phi\colon E\lra L$ which includes the so-called
Bradlow pairs. For the representation of $\GL(r)$ on $S^2\C^3$ we find the
conic bundles of Gomez and Sols. In the present paper, we will formulate a
general semistability concept for the above triples which depends on a rational
parameter $\delta$ and establish the existence of moduli spaces of
$\delta$-(semi)stable triples of fixed topological type. The notion of
semistability mimics the Hilbert-Mumford criterion for $SL(r)$ which is the
main reason that such a general approach becomes feasible. In the known
examples (the above, Higgs bundles, extension pairs, oriented framed bundles)
we show how to recover the "usual" semistability concept. This process of
simplification can also be formalized. Altogether, our results provide a
unifying construction for the moduli spaces of most decorated vector bundle
problems together with an automatism for finding the right notion of
semistability and should therefore be of some interest.Comment: Final Version (To appear in Transformation Groups); V2: Example 3.7
corrected, other minor modifications; V3: Notion of polystability corrected,
other minor modification | A universal construction for moduli spaces of decorated vector bundles
over curves | a universal construction for moduli spaces of decorated vector bundles over curves | projective numbers. colon satisfies integer alpha alpha associate classifying triples bundle bundle colon trivial homomorphism. bundle classify triples consisting homomorphism colon bradlow pairs. conic bundles gomez sols. formulate semistability triples rational delta establish moduli delta triples topological type. notion semistability mimics hilbert mumford criterion feasible. bundles oriented framed bundles recover usual semistability concept. simplification formalized. altogether unifying moduli decorated bundle automatism notion semistability corrected minor modifications notion polystability corrected minor modification | non_dup | [] |
2583409 | 10.1007/s00031-005-0402-4 | We construct the action of the quantum group U_v(sl_n) by the natural
correspondences in the equivariant localized $K$-theory of the Laumon based
Quasiflags' moduli spaces. The resulting module is the universal Verma module.
We construct geometrically the Shapovalov scalar product and the Whittaker
vectors. It follows that a certain generating function of the characters of the
global sections of the structure sheaves of the Laumon moduli spaces satisfies
a $v$-difference analogue of the quantum Toda lattice system, reproving the
main theorem of Givental-Lee. The similar constructions are performed for the
affine Lie agebra \hat{sl}_n.Comment: Some corrections are made in Sections 2, | Finite difference quantum Toda lattice via equivariant K-theory | finite difference quantum toda lattice via equivariant k-theory | correspondences equivariant localized laumon quasiflags moduli spaces. module universal verma module. geometrically shapovalov whittaker vectors. generating characters sheaves laumon moduli satisfies analogue toda reproving givental lee. constructions affine agebra | non_dup | [] |
2572052 | 10.1007/s00031-005-1101-x | Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e.,
a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring
k[x_{ij}]), and adj(X) its classical adjoint. It is shown that if char k=0 and
n is odd, then adj(X) is not the product of two noninvertible nxn matrices over
k[x_{ij}]. If n is even and >2, a restricted class of nontrivial factorizations
occur. The nonzero-characteristic case remains open.
The operation adj on matrices arises from the (n-1)st exterior power functor
on modules; the same question can be posed for matrix operations arising from
other functors.Comment: Revised version contains answer to "even n" question left open in
original version. (Answer due to Buchweitz & Leuschke; simple proof in this
note.) Copy at http://math.berkeley.edu/~gbergman/papers will always have
latest version; revisions sent to arXiv only for major change | Can one factor the classical adjoint of a generic matrix? | can one factor the classical adjoint of a generic matrix? | integer generic i.e. indeterminates adjoint. char noninvertible restricted nontrivial factorizations occur. nonzero open. arises exterior functor modules posed operations arising revised answer version. answer buchweitz leuschke note. copy gbergman papers latest revisions sent | non_dup | [] |
2581364 | 10.1007/s00031-005-1107-4 | We study a generalization of the isomonodromic deformation to the case of
connections with irregular singularities. We call this generalization Isostokes
Deformation. A new deformation parameter arises: one can deform the formal
normal forms of connections at irregular points. We study this part of the
deformation, giving an algebraic description. Then we show how to use loop
groups and hypercohomology to write explicit hamiltonians. We work on an
arbitrary complete algebraic curve, the structure group is an arbitrary
semisimiple group.Comment: 23 pages, minor corrections in the introduction, references expande | Algebraic and hamiltonian approaches to isostokes deformations | algebraic and hamiltonian approaches to isostokes deformations | generalization isomonodromic deformation connections irregular singularities. call generalization isostokes deformation. deformation arises deform formal connections irregular points. deformation giving algebraic description. hypercohomology hamiltonians. algebraic semisimiple pages minor expande | non_dup | [] |
2584412 | 10.1007/s00031-005-1116-3 | Let G be a complex reductive group. A normal G-variety X is called spherical
if a Borel subgroup of G has a dense orbit in X. Of particular interest are
spherical varieties which are smooth and affine since they form local models
for multiplicity free Hamiltonian K-manifolds, K a maximal compact subgroup of
G. In this paper, we classify all smooth affine spherical varieties up to
coverings, central tori, and C*-fibrations.Comment: v1: 23 pages, uses texdraw; v2: 25 pages, introduction updated, Lemma
7.2 fixed, references added, typos correcte | Classification of smooth affine spherical varieties | classification of smooth affine spherical varieties | reductive group. spherical borel subgroup dense orbit spherical varieties affine multiplicity manifolds maximal subgroup classify affine spherical varieties coverings tori pages texdraw pages updated typos correcte | non_dup | [] |
36025335 | 10.1007/s00031-005-1124-3 | 34 pages.-- MSC codes: 53C30; 53C26.-- Printed version published Dec 2006.-- ArXiv pre-print available at: http://arxiv.org/abs/math/0504550An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the\ud
representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is characterised by admitting homogeneous structures of a particularly simple type. In the process we\ud
study the properties of different homogeneous models for HH(n).Partially supported by DGICYT, Spain, under Grant MTM2005-00173. Partially supported by the EDGE, Research Training Network HPRN-CT-2000-0010, of the European Human Potential Programme.Peer reviewe | Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic space | homogeneous quaternionic kaehler structures and quaternionic hyperbolic space | pages. codes printed print homogeneous quaternionic kaehler tensors relate theoretic fino. quaternionic hyperbolic characterised admitting homogeneous type. homogeneous .partially dgicyt spain partially hprn programme.peer reviewe | non_dup | [] |
2593622 | 10.1007/s00031-005-1125-2 | We study the composition of the functor from the category of modules over the
Lie algebra gl_m to the category of modules over the degenerate affine Hecke
algebra of GL_N introduced by I. Cherednik, with the functor from the latter
category to the category of modules over the Yangian Y(gl_n) due to V.
Drinfeld. We propose a representation theoretic explanation of a link between
the intertwining operators on the tensor products of Y(gl_n)-modules, and the
`extremal cocycle' on the Weyl group of gl_m defined by D. Zhelobenko. We also
establish a connection between the composition of two functors, and the
`centralizer construction' of the Yangian Y(gl_n) discovered by G. Olshanski.Comment: publication details added. arXiv admin note: substantial text overlap
with arXiv:math/060627 | Yangians and Mickelsson Algebras I | yangians and mickelsson algebras i | functor modules modules degenerate affine hecke cherednik functor modules yangian drinfeld. propose theoretic explanation intertwining modules extremal cocycle weyl zhelobenko. establish connection functors centralizer yangian discovered publication added. admin substantial overlap math | non_dup | [] |
2584917 | 10.1007/s00031-005-1127-0 | Using methods applied by Atiyah in equivariant K-theory, Bredon obtained
exact sequences for the relative cohomologies (with rational coefficients) of
the equivariant skeletons of (sufficiently nice) T-spaces, T=(S^1)^n, with free
equivariant cohomology over the cohomology of BT. Here we characterise those
finite T-CW complexes with connected isotropy groups for which an analogous
result holds with integral coefficients.Comment: similar main result as in our preprint math.AT/0307112, but the proof
is more elementary; 10 pages; final versio | Exact cohomology sequences with integral coefficients for torus actions | exact cohomology sequences with integral coefficients for torus actions | atiyah equivariant bredon cohomologies rational equivariant skeletons sufficiently nice equivariant cohomology cohomology characterise complexes isotropy analogous preprint math.at elementary pages versio | non_dup | [] |
2588533 | 10.1007/s00031-006-0051-2 | In two 1966 papers, Jacques Tits gave a construction of exceptional Lie
algebras (hence implicitly exceptional algebraic groups) and a classification
of possible indexes of simple algebraic groups. For the special case of his
construction that gives groups of type E6, we connect the two papers by
answering the question: Given an Albert algebra A and a separable quadratic
field extension K, what is the index of the resulting algebraic group?Comment: 29 pages. For possibly newer versions, see
http://www.mathcs.emory.edu/~skip/preprints.htm | Groups of outer type E6 with trivial Tits algebras | groups of outer type e6 with trivial tits algebras | papers jacques tits gave exceptional algebras implicitly exceptional algebraic indexes algebraic groups. connect papers answering albert separable quadratic algebraic comment pages. possibly newer versions skip preprints.htm | non_dup | [] |
2594159 | 10.1007/s00031-007-0057-4 | A visible action on a complex manifold is a holomorphic action that admits a
$J$-transversal totally real submanifold $S$.
It is said to be strongly visible if there exists an orbit-preserving
anti-holomorphic diffeomorphism $\sigma$ such that $\sigma |_S = \mathrm{id}$.
In this paper, we prove that for any Hermitian symmetric space $D = G/K$ the
action of any symmetric subgroup $H$ is strongly visible.
The proof is carried out by finding explicitly an orbit-preserving
anti-holomorphic involution and a totally real submanifold $S$.
Our geometric results provide a uniform proof of various multiplicity-free
theorems of irreducible highest weight modules when restricted to reductive
symmetric pairs, for both classical and exceptional cases, for both finite and
infinite dimensional cases, and for both discrete and continuous spectra | Visible actions on symmetric spaces | visible actions on symmetric spaces | visible manifold holomorphic admits transversal totally submanifold said visible orbit preserving holomorphic diffeomorphism sigma sigma mathrm hermitian subgroup visible. explicitly orbit preserving holomorphic involution totally submanifold geometric multiplicity theorems irreducible modules restricted reductive exceptional infinite | non_dup | [] |
2594528 | 10.1007/s00031-007-0061-8 | We describe a stratification on the double flag variety $G/B^+\times G/B^-$
of a complex semisimple algebraic group $G$ analogous to the Deodhar
stratification on the flag variety $G/B^+$, which is a refinement of the
stratification into orbits both for $B^+\times B^-$ and for the diagonal action
of $G$, just as Deodhar's stratification refines the orbits of $B^+$ and $B^-$.
We give a coordinate system on each stratum, and show that all strata are
coisotropic subvarieties. Also, we discuss possible connections to the positive
and cluster geometry of $G/B^+\times G/B^-$, which would generalize results of
Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double
Schubert cells.Comment: 21 page | A Deodhar type stratification on the double flag variety | a deodhar type stratification on the double flag variety | stratification flag semisimple algebraic analogous deodhar stratification flag refinement stratification orbits diagonal deodhar stratification refines orbits coordinate stratum strata coisotropic subvarieties. connections generalize fomin zelevinsky bruhat marsh rietsch schubert | non_dup | [] |
2598978 | 10.1007/s00031-008-9006-0 | Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly
isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property
$({\BP}_0^V)$, for $V$ be a Banach space: a locally compact group $G$ has
property $({\BP}_0^V)$ if every affine isometric action of $G$ on $V$, such
that the linear part is a $C_0$-representation of $G$, either has a fixed point
or is metrically proper. We prove that solvable groups, connected Lie groups,
and linear algebraic groups over a local field of characteristic zero, have
property $({\BP}_0^V)$. As a consequence for unitary representations, we
characterize those groups in the latter classes for which the first cohomology
with respect to the left regular representation on $L^2(G)$ is non-zero; and we
characterize uniform lattices in those groups for which the first $L^2$-Betti
number is non-zero.Comment: 28 page | Isometric group actions on Banach spaces and representations vanishing
at infinity | isometric group actions on banach spaces and representations vanishing at infinity | acts properly isometrically banach locally affine isometric metrically proper. solvable algebraic unitary representations characterize cohomology characterize lattices betti | non_dup | [] |
1936728 | 10.1007/s00031-008-9009-x | We compute the integral cohomology of the minimal non-trivial nilpotent orbit
in a complex simple (or quasi-simple) Lie algebra. We find by a uniform
approach that the middle cohomology group is isomorphic to the fundamental
group of the sub-root system generated by the long simple roots. The modulo
$\ell$ reduction of the Springer correspondent representation involves the sign
representation exactly when $\ell$ divides the order of this cohomology group.
The primes dividing the torsion of the rest of the cohomology are bad primes.Comment: 29 pages, v2 : Leray-Serre spectral sequence replaced by Gysin
sequence only, corrected typo | Cohomology of the minimal nilpotent orbit | cohomology of the minimal nilpotent orbit | cohomology trivial nilpotent orbit quasi algebra. cohomology isomorphic roots. modulo springer correspondent involves divides cohomology group. primes dividing torsion cohomology pages leray serre replaced gysin corrected typo | non_dup | [] |
1964029 | 10.1007/s00031-008-9037-6 | We construct natural selfmaps of compact cohomgeneity one manifolds with
finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds
with simple cohomology rings this yields in certain cases relations between the
order of the Weyl group and the Euler characteristic of a principal orbit. We
apply our construction to the compact Lie group SU(3) where we extend identity
and transposition to an infinite family of selfmaps of every odd degree. The
compositions of these selfmaps with the power maps realize all possible degrees
of selfmaps of SU(3).Comment: v2, v3: minor improvement | Cohomogeneity one manifolds and selfmaps of nontrivial degree | cohomogeneity one manifolds and selfmaps of nontrivial degree | selfmaps cohomgeneity manifolds weyl lefschetz numbers. manifolds cohomology rings weyl euler principal orbit. extend transposition infinite selfmaps degree. compositions selfmaps realize selfmaps .comment minor | non_dup | [] |
2030240 | 10.1007/s00031-010-9089-2 | Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo | Affine T-varieties of complexity one and locally nilpotent derivations | affine t-varieties of complexity one and locally nilpotent derivations | spec affine algebraically endowed torus homogeneous locally nilpotent derivation affine graded generates action. toric varieties generalizes flenner zaidenberg. homogeneous makar limanov varieties. exhibit rational varieties trivial makar limanov pages. minor structure. typo | non_dup | [] |
4434351 | 10.1007/s00031-010-9103-8 | We compute the space of Poisson traces on a classical W-algebra, i.e., linear functionals invariant under Hamiltonian derivations. Modulo any central character, this space identifies with the top cohomology of the corresponding Springer fiber. As a consequence, we deduce that the zeroth Hochschild homology of the corresponding quantum W-algebra modulo a central character identifies with the top cohomology of the corresponding Springer fiber. This implies that the number of irreducible finite-dimensional representations of this algebra is bounded by the dimension of this top cohomology, which was established earlier by C. Dodd using reduction to positive characteristic. Finally, we prove that the entire cohomology of the Springer fiber identifies with the so-called Poisson-de Rham homology (defined previously by the authors) of the centrally reduced classical W-algebra.National Science Foundation (U.S.) (grant DMS-0504847)National Science Foundation (U.S.) (grant DMS-0900233 | Traces on finite W-algebras | traces on finite w-algebras | poisson traces i.e. functionals derivations. modulo character identifies cohomology springer fiber. deduce zeroth hochschild homology modulo character identifies cohomology springer fiber. irreducible representations cohomology dodd characteristic. cohomology springer fiber identifies poisson rham homology centrally algebra.national foundation u.s. foundation u.s. | non_dup | [] |
2066655 | 10.1007/s00031-011-9120-2 | Let G be a simply connected semisimple algebraic group over an algebraically
closed field k of characteristic 0 and let V be a rational simple G-module of
finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its
closure, then we describe the orbits of X and those of its normalization. If
moreover the wonderful completion of G/H is strict, then we give necessary and
sufficient combinatorial conditions so that the normalization morphism is a
homeomorphism. Such conditions are trivially fulfilled if G is simply laced or
if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation
Groups. Simplified some proofs and corrected minor mistakes, added
references. v3: major changes due to a mistake in previous version | Spherical orbit closures in simple projective spaces and their
normalizations | spherical orbit closures in simple projective spaces and their normalizations | semisimple algebraic algebraically rational module dimension. spherical orbit closure orbits normalization. wonderful completion strict combinatorial normalization morphism homeomorphism. trivially fulfilled laced pages latex. groups. simplified proofs corrected minor mistakes references. mistake | non_dup | [] |
2106249 | 10.1007/s00031-011-9127-8 | We study a type of left-invariant structure on Lie groups, or equivalently on
Lie algebras. We introduce obstructions to the existence of a hypo structure,
namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy
SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain
associated cohomology groups, determine a first obstruction. We also construct
necessary conditions for the existence of a hypo structure with a fixed
almost-contact form. For non-unimodular Lie algebras, we derive an obstruction
to the existence of a hypo structure, with no choice involved. We apply these
methods to classify solvable Lie algebras that admit a hypo structure.Comment: 21 pages; v2: presentation improved, typos corrected, notational
conflicts eliminated. To appear in Transformation Group | Solvable Lie algebras are not that hypo | solvable lie algebras are not that hypo | equivalently algebras. obstructions hypo hypersurfaces manifolds holonomy splitting vanishing cohomology obstruction. hypo form. unimodular algebras derive obstruction hypo involved. classify solvable algebras admit hypo pages presentation typos corrected notational conflicts eliminated. | non_dup | [] |
2104292 | 10.1007/s00031-011-9131-z | Automorphism groups of locally finite trees provide a large class of examples
of simple totally disconnected locally compact groups. It is desirable to
understand the connections between the global and local structure of such a
group. Topologically, the local structure is given by the commensurability
class of a vertex stabiliser; on the other hand, the action on the tree
suggests that the local structure should correspond to the local action of a
stabiliser of a vertex on its neighbours.
We study the interplay between these different aspects for the special class
of groups satisfying Tits' independence property. We show that such a group has
few open subgroups if and only if it acts locally primitively. Moreover, we
show that it always admits many germs of automorphisms which do not extend to
automorphisms, from which we deduce a negative answer to a question by George
Willis. Finally, under suitable assumptions, we compute the full group of germs
of automorphisms; in some specific cases, these turn out to be simple and
compactly generated, thereby providing a new infinite family of examples which
generalise Neretin's group of spheromorphisms. Our methods describe more
generally the abstract commensurator group for a large family of
self-replicating profinite branch groups | Simple locally compact groups acting on trees and their germs of
automorphisms | simple locally compact groups acting on trees and their germs of automorphisms | automorphism locally trees totally disconnected locally groups. desirable connections group. topologically commensurability stabiliser stabiliser neighbours. interplay satisfying tits independence property. subgroups acts locally primitively. admits germs automorphisms extend automorphisms deduce answer george willis. assumptions germs automorphisms compactly thereby infinite generalise neretin spheromorphisms. commensurator replicating profinite branch | non_dup | [] |
2189877 | 10.1007/s00031-011-9167-0 | Given a holomorphic line bundle over the complex affine quadric $Q^2$, we
investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant
biholomorphism, these are all contained in a maximal one, say $\Omega_{max}$.
By removing the zero section to $\Omega_{max}$ one obtains the unique Stein,
SU(2)-equivariant, punctured disc bundle over $Q^2$ which contains entire
curves. All other such punctured disc bundles are shown to be Kobayashi
hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group | On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the
complex affine quadric | on hyperbolicity of su(2)-equivariant, punctured disc bundles over the complex affine quadric | holomorphic bundle affine quadric stein equivariant disc bundles. equivariant biholomorphism maximal omega removing omega obtains stein equivariant punctured disc bundle curves. punctured disc bundles kobayashi pages minor | non_dup | [] |
2180701 | 10.1007/s00031-012-9174-9 | Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona
group are studied. Infinitely many non-conjugate embeddings which preserve the
type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements
of the same type) are provided. The existence of infinitely many non-conjugate
elliptic, parabolic and hyperbolic embeddings is also shown.
In particular, a group G of automorphisms of a smooth surface S obtained by
blowing-up 10 points of the complex projective plane is given. The group G is
isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of
infinite order are hyperbolic.Comment: to appear in Transformation Group | Embeddings of SL(2,Z) into the Cremona group | embeddings of sl(2,z) into the cremona group | geometric embeddings cremona studied. infinitely conjugate embeddings preserve i.e. send elliptic parabolic hyperbolic provided. infinitely conjugate elliptic parabolic hyperbolic embeddings shown. automorphisms blowing projective given. isomorphic preserves elliptic infinite | non_dup | [] |
2185113 | 10.1007/s00031-012-9176-7 | We classify Nichols algebras of irreducible Yetter-Drinfeld modules over
groups such that the underlying rack is braided and the homogeneous component
of degree three of the Nichols algebra satisfies a given inequality. This
assumption turns out to be equivalent to a factorization assumption on the
Hilbert series. Besides the known Nichols algebras we obtain a new example. Our
method is based on a combinatorial invariant of the Hurwitz orbits with respect
to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure | Braided racks, Hurwitz actions and Nichols algebras with many cubic
relations | braided racks, hurwitz actions and nichols algebras with many cubic relations | classify nichols algebras irreducible yetter drinfeld modules rack braided homogeneous nichols satisfies inequality. turns factorization hilbert series. besides nichols algebras example. combinatorial hurwitz orbits braid pages tables | non_dup | [] |
2136335 | 10.1007/s00031-012-9178-5 | In the present paper we introduce and study the notion of an equivariant
pretheory: basic examples include equivariant Chow groups, equivariant K-theory
and equivariant algebraic cobordism. To extend this set of examples we define
an equivariant (co)homology theory with coefficients in a Rost cycle module and
provide a version of Merkurjev's (equivariant K-theory) spectral sequence for
such a theory. As an application we generalize the theorem of
Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a
G-equivariant pretheory we associate a graded ring which serves as an invariant
of E. In the case of Chow groups this ring encodes the information concerning
the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes
of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous
preprint: the construction of an equivariant cycle (co)homology and the
spectral sequence (generalizing the long exact localization sequence) are
adde | Equivariant pretheories and invariants of torsors | equivariant pretheories and invariants of torsors | notion equivariant pretheory equivariant chow equivariant equivariant algebraic cobordism. extend equivariant homology rost module merkurjev equivariant theory. generalize karpenko merkurjev torsors rational cycles torsor equivariant pretheory associate graded serves chow encodes concerning motivic grothendieck indexes respective tits pages essentially preprint equivariant homology generalizing localization adde | non_dup | [] |
2136034 | 10.1007/s00031-012-9181-x | In this paper we study the structure of cohomology spaces for the Frobenius
kernels of unipotent and parabolic algebraic group schemes and of their quantum
analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and
its unipotent radical $U_J$, we determine the ring structure of the cohomology
ring $H^\bullet((U_J)_1,k)$. We also obtain new results on computing
$H^\bullet((P_J)_1,L(\lambda))$ as an $L_J$-module where $L(\lambda)$ is a
simple $G$-module with high weight $\lambda$ in the closure of the bottom
$p$-alcove. Finally, we provide generalizations of all our results to the
quantum situation.Comment: 18 pages. Some proofs streamlined over previous version. Additional
details added to some proofs in Section | Cohomology for infinitesimal unipotent algebraic and quantum groups | cohomology for infinitesimal unipotent algebraic and quantum groups | cohomology frobenius kernels unipotent parabolic algebraic schemes analogs. algebraic parabolic subgroup unipotent radical cohomology bullet bullet lambda module lambda module lambda closure alcove. generalizations pages. proofs streamlined version. proofs | non_dup | [] |
2187089 | 10.1007/s00031-012-9184-7 | Let G be a simple algebraic group over an algebraically closed field of good
odd characteristic, and let theta be an automorphism of G arising from an
involution of its Dynkin diagram. We show that the spherical theta-twisted
conjugacy classes are precisely those intersecting only Bruhat cells
corresponding to twisted involutions in the Weyl group. We show how the
analogue of this statement fails in the triality case. We generalize to good
odd characteristic J-H. Lu's dimension formula for spherical twisted conjugacy
classes.Comment: proof of Lemma 6.4 polished. The journal version is available at
http://www.springerlink.com/content/k573l88256753640 | On spherical twisted conjugacy classes | on spherical twisted conjugacy classes | algebraic algebraically theta automorphism arising involution dynkin diagram. spherical theta twisted conjugacy precisely intersecting bruhat twisted involutions weyl group. analogue statement fails triality case. generalize spherical twisted conjugacy polished. | non_dup | [] |
2255074 | 10.1007/s00031-012-9202-9 | We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact
groups. By using a degeneration based on the Vinberg monoid we give, in good
cases, a global quotient description of a surgery construction introduced by
Woodward and Meinrenken, and show it can be interpreted in algebro-geometric
terms. A key ingredient is the `universal cut' of the cotangent bundle of the
group itself, which is identified with a moduli space of framed bundles on
chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8
figure | On Non-Abelian Symplectic Cutting | on non-abelian symplectic cutting | symplectic cutting abelian groups. degeneration vinberg monoid quotient woodward meinrenken interpreted algebro geometric terms. ingredient universal cotangent bundle moduli framed bundles chains projective edits groups. pages | non_dup | [] |
6206769 | 10.1007/s00031-013-9221-1 | We use equivariant localization and divided difference operators to determine
formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit
closures on the flag variety $G/B$, where $G = GL(n,\C)$, and where $K$ is one
of the symmetric subgroups $O(n,\C)$ or $Sp(n,\C)$. We realize these orbit
closures as universal degeneracy loci for a vector bundle over a variety
equipped with a single flag of subbundles and a nondegenerate symmetric or
skew-symmetric bilinear form taking values in the trivial bundle. We describe
how our equivariant formulas can be interpreted as giving formulas for the
classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version,
to appear in Transformation Group | K-orbit closures on G/B as universal degeneracy loci for flagged vector
bundles with symmetric or skew-symmetric bilinear form | k-orbit closures on g/b as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form | equivariant localization divided formulas torus equivariant cohomology orbit closures flag subgroups realize orbit closures universal degeneracy loci bundle equipped flag subbundles nondegenerate skew bilinear trivial bundle. equivariant formulas interpreted giving formulas loci chern minor revisions referees. | non_dup | [] |
5255578 | 10.1007/s00031-013-9240-y | We construct and study a family of toric degenerations of the algebra of
conformal blocks for a stable marked curve $(C, \vec{p})$ with structure group
$SL_3(\mathbb{C}).$ We find that this algebra is Gorenstein. For the genus $0,
1$ cases we find the level of conformal blocks necessary to generate the
algebra. In the genus 0 case we also find bounds on the degrees of relations
required to present the algebra. Along the way we recover polyhedral rules for
counting conformal blocks originally due to Senechal, Mathieu, Kirillov, and
Walton.Comment: 22 pages, 13 figure | The algebra of $SL_3(\mathbb{C})$ conformal blocks | the algebra of $sl_3(\mathbb{c})$ conformal blocks | toric degenerations conformal blocks marked mathbb gorenstein. genus conformal blocks algebra. genus bounds algebra. recover polyhedral counting conformal blocks originally senechal mathieu kirillov pages | non_dup | [] |
51959792 | 10.1007/s00031-014-9253-1 | International audienceLet $W$ be a finite-dimensional representation of a reductive algebraic group $G$. The invariant Hilbert scheme $\mathcal{H}$ is a moduli space that classifies the $G$-stable closed subschemes $Z$ of $W$ such that the affine algebra $k[Z]$ is the direct sum of simple $G$-modules with prescribed multiplicities. In this article, we consider the case where $G$ is a classical group acting on a classical representation $W$ and $k[Z]$ is isomorphic to the regular representation of $G$ as a $G$-module. We obtain families of examples where $\mathcal{H}$ is a smooth variety, and thus for which the Hilbert-Chow morphism $\gamma: \mathcal{H} \rightarrow W//G$ is a canonical desingularization of the categorical quotient | Invariant Hilbert schemes and desingularizations of quotients by classical groups | invariant hilbert schemes and desingularizations of quotients by classical groups | audiencelet reductive algebraic hilbert mathcal moduli classifies subschemes affine modules prescribed multiplicities. acting isomorphic module. families mathcal hilbert chow morphism gamma mathcal rightarrow canonical desingularization categorical quotient | non_dup | [] |
78058183 | 10.1007/s00031-014-9260-2 | P. Deligne defined interpolations of the tensor category of representations of the symmetric group S [subscript n] to complex values of n. Namely, he defined tensor categories Rep(S [subscript t]) for any complex t. This construction was generalized by F. Knop to the case of wreath products of S[subscript n] with a finite group. Generalizing these results, we propose a method of interpolating representation categories of various algebras containing S [subscript n] (such as degenerate affine Hecke algebras, symplectic reflection algebras, rational Cherednik algebras, etc.) to complex values of n. We also define the group algebra of S [subscript n] for complex n, study its properties, and propose a Schur-Weyl duality for Rep(S [subscript t]).National Science Foundation (U.S.) (Grant DMS-0504847)National Science Foundation (U.S.) (Grant DMS-1000113 | Representation Theory in Complex Rank, I | representation theory in complex rank, i | deligne interpolations representations subscript categories subscript knop wreath subscript group. generalizing propose interpolating categories algebras subscript degenerate affine hecke algebras symplectic reflection algebras rational cherednik algebras etc. subscript propose schur weyl duality subscript .national foundation u.s. foundation u.s. | non_dup | [] |
83228173 | 10.1007/s00031-014-9263-z | We show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra sℓˆ[subscript 2|1] (resp. psℓˆ[subscript 2|2]) can be modified, using Zwegers’ real analytic corrections, to form a modular (resp. S-) invariant family of functions. Applying the quantum Hamiltonian reduction, this leads to a new family of positive energy modules over the N = 2 (resp.N = 4) superconformal algebras with central charge 3(1 − (2 m + 2)/M), where m ∈ ℤ[subscript ≥0], M ∈ ℤ[subscript ≥2], gcd(2 m + 2, M) = 1 if m > 0 (resp. 6 (m/M − 1), where m ∈ ℤ[subscript ≥1], M ∈ ℤ[subscript ≥2], gcd(2 m, M) = 1 if m > 1), whose modified characters and supercharacters form a modular invariant family | REPRESENTATIONS OF AFFINE SUPERALGEBRAS AND MOCK THETA FUNCTIONS | representations of affine superalgebras and mock theta functions | supercharacters principal admissible modules affine superalgebra subscript resp. psℓˆ subscript zwegers’ analytic modular resp. functions. modules resp.n superconformal algebras subscript subscript resp. subscript subscript characters supercharacters modular | non_dup | [] |