a paley wiener theorem for real reductive groups le groupe sl 3 r prequantification des orbites de dimension minimale parmi celles non triviales dans la representation co adjointe de sl 3 r noyaux de blattner kostant steinberg irreductibilite et unicite du prolongement de certaines representations de p 3 a sl 3 r etude du prolongement des representations e a sl 3 r la representation type s s 2 minimal parametres de langlands et operateur d entrelacement avec la serie principale pour les representations e et

classical sheaf cohomology rings on grassmannians abstract let the vector bundle e be a deformation of the tangent bundle over the grassmannian g k n we compute the ring structure of sheaf cohomology valued in exterior powers of e also known as the polymology this is the first part of a project studying the quantum sheaf cohomology of grassmannians with deformations of the tangent bundle a generalization of ordinary quantum cohomology rings of grassmannians a companion physics paper 6 describes physical aspects of the theory including a conjecture for the quantum sheaf cohomology ring and numerous examples

elliptic genera of 2d mathcal n 2 gauge theories we compute the elliptic genera of general two dimensional mathcal n 2 2 and mathcal n 0 2 gauge theories we find that the elliptic genus is given by the sum of jeffrey kirwan residues of a meromorphic form representing the one loop determinant of fields on the moduli space of flat connections on t2 we give several examples illustrating our formula with both abelian and non abelian gauge groups and discuss some dualities for u k and su k theories this paper is a sequel to the authors previous paper benini et al lett math phys 104 465 493 2014

elliptic modular double and 4d partition functions we consider 4d supersymmetric special unitary gamma quiver gauge theories on compact manifolds which are t 2 fibrations over s 2 we show that their partition functions are correlators of vertex

intertwining operators and residues i weighted characters operateurs d entrelacement normalisation groupes reels groupes p adiques representations standard les distributions j m la distribution j m x residus changements de contour les espaces 7b h ac g f s et 7b f ac g f s l application m

quantum sheaf cohomology and duality of flag manifolds we study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds realized as the ope ring of a 2 twisted two dimensional theories with 0 2 supersymmetry quantum sheaf cohomology generalizes the notion of quantum cohomology complete descriptions of quantum sheaf cohomology have been obtained for abelian gauged linear sigma models glsms and for nonabelian glsms describing grassmannians in this paper we continue to explore the quantum sheaf cohomology of nonabelian theories we first propose a method to compute the generating relations for 0 2 glsms with 2 2 locus we apply this method to derive the quantum sheaf cohomology of products of grassmannians and flag manifolds the dual deformation associated with the biholomorphic duality gives rise to an explicit ir duality of two a 2 twisted 0 2 gauge theories

parabolic transfer for real groups this paper is the second of two articles in real harmonic analysis in the first paper a14 we established asymptotic formulas for some natural distributions on a real group in this paper we shall establish important relationships among the distributions as the group varies the group is the set of real points of a connected reductive group g over r the distributions are weighted orbital integrals jm f on g r and their invariant counterparts im f here m g is a levi subgroup of g while mg reg r is a strongly g regular conjugacy class in m r the relationships are defined by the invariant transfer of functions on g r to functions attached to endoscopic groups of g this necessitates our working with the invariant distributions im f we refer the reader to the introduction of a14 for some general remarks on these objects the distributions im f are the generic archimedean terms in the invariant trace formula we cannot review the trace formula here the reader might consult the introductions to a13 and its two predecessors for a brief summary the purpose of the paper a13 was to stabilize the invariant trace formula subject to a condition on the fundamental lemma that has been established in some special cases the stable trace formula is a milestone of sorts it is expected to lead to reciprocity laws which relate fundamental arithmetic data attached to automorphic representations on different groups the stable trace formula of a13 relies upon the results of this paper as well as a paper a16 in preparation this has been our guiding motivation the relevant identities among the nonarchimedean forms of the distributions im f were actually established in a13 they were a part of the global argument that culminated in the stable trace formula as such they are subject to the condition on the fundamental lemma mentioned above our goal here is to establish the outstanding archimedean identities we shall do so by purely local means which are independent of the fundamental lemma to simplify the introducton we assume that the derived group of g is simply connected the identities then relate the invariant distributions ong r with stable distributions on endoscopic groups g r we recall that a stable distribution on g r depends only on the average values assumed by a test function over strongly regular stable conjugacy classes in greg r which is to say intersections of g reg r

global aspects of 0 2 moduli space toric varieties and tangent bundles we study the moduli space of a 2 half twisted gauged linear sigma models for nef fano toric varieties focusing on toric deformations of the tangent bundle we describe the vacuum structure of many 0 2 theories in particular identifying loci in parameter space with spontaneous supersymmetry breaking or divergent ground ring correlators we find that the parameter space of such an a 2 theory and its ground ring is in general a moduli stack and we show in examples that with suitable stability conditions it is possible to obtain a simple compactification of the moduli space of smooth a 2 theories

two sphere partition functions and gromov witten invariants many n 2 2 two dimensional nonlinear sigma models with calabi yau target spaces admit ultraviolet descriptions as n 2 2 gauge theories gauged linear sigma models we conjecture that the two sphere partition function of such ultraviolet gauge theories recently computed via localization by benini et al and doroud et al yields the exact kahler potential on the quantum kahler moduli space for calabi yau threefold target spaces in particular this allows one to compute the genus zero gromov witten invariants for any such calabi yau threefold without the use of mirror symmetry more generally when the infrared superconformal fixed point is used to compactify string theory this provides a direct method to compute the spacetime kahler potential of certain moduli e g vector multiplet moduli in type iia exactly in we compute these quantities for the quintic and for rodland s pfaffian calabi yau threefold and find agreement with existing results in the literature we then apply our methods to a codimension four determinantal calabi yau threefold in p 7 recently given a nonabelian gauge theory description by the present authors for which no mirror calabi yau is currently known we derive predictions for its gromov witten invariants and verify that our predictions satisfy nontrivial geometric checks

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

notes on certain 0 2 correlation functions in this paper we shall describe some correlation function computations in perturbative heterotic strings that for example in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of elements of dolbeault cohomology groups on the target space the heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups one must not only compactify moduli spaces of rational curves but also extend a sheaf determined by the gauge bundle over the compactification and linear sigma models provide natural mechanisms for doing both euler classes of obstruction bundles generalize to this language in an interesting way

toric reduction and a conjecture of batyrev and materov this paper grew out of our efforts to understand the toric residue mirror conjecture formulated by batyrev and materov in 2 this conjecture has its origin in physics and is based on a work by morrison and plesser 14 according to the philosophy of mirror symmetry to every manifold in a certain class one can associate a dual manifold the so called mirror so that the intersection numbers of the moduli spaces of holomorphic curves in one of these manifolds are related to integrals of certain special differential forms on the other while at the moment this mirror manifold is only partially understood there is an explicit construction due to victor batyrev 1 in which the two manifolds are toric varieties whose defining data are related by a natural duality notion for polytopes let us recall the setting of the conjecture of batyrev and materov let t be a d dimensional real vector space endowed with an integral structure a lattice t t of full rank we denote by t the embedded dual lattice v t v z for all t consider two convex polytopes t and t containing the origin in their respective interiors and related by the duality

partition functions of n 2 2 gauge theories on s 2 and vortices we apply localization techniques to compute the partition function of a two dimensional mathcal n 2 2 r symmetric theory of vector and chiral multiplets on s2 the path integral reduces to a sum over topological sectors of a matrix integral over the cartan subalgebra of the gauge group for gauge theories which would be completely higgsed in the presence of a fayet iliopoulos term in flat space the path integral alternatively reduces to the product of a vortex times an antivortex partition functions weighted by semiclassical factors and summed over isolated points on the higgs branch for applications we evaluate the partition function for some u n gauge theories showing equality of the path integrals for theories conjectured to be dual by hori and tong and deriving new expressions for vortex partition functions

topological field theory and rational curves we analyze the quantum field theory corresponding to a string propagating on a calabi yau threefold this theory naturally leads to the consideration of witten s topological non linear model and the structure of rational curves on the calabi yau manifold we study in detail the case of the world sheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in agreement with a conjecture by candelas de la ossa green and parkes

a stratification related to characteristic polynomials abstract we shall describe two problems in beyond endoscopy the strategy advanced by langlands for bringing the trace formula to bear on the general principle of functoriality one is to be able to apply the poisson summation formula to the regular elliptic part of the trace formula for a general linear group gl n 1 the other is to be able to recognize the spectral contribution of the nontempered discrete spectrum to the resulting geometric expansion

discrete series characters and fourier inversion on semisimple real lie groups let g be a semisimple real lie group explicit formulas for discrete series characters on noncompact cartan subgroups are given these formulas are used to give a simple formula for the fourier transform of orbital integrals of regular semisimple orbits

noninvariant integrals on semisimple groups of r rank one integrales invariantes et non invariantes definition et proprietes integrales d eisenstein et paquets d onde quelques estimations elementaires application aux asymptotes le role du terme constant utilisation des equations differentielles operateurs d entrelacement et c fonctions definition et proprietes de la transformee de fourier interpretation des calculs elimination de la k finitude isolation de centralite passage a la limite

quantum sheaf cohomology on grassmannians in this paper we study the quantum sheaf cohomology of grassmannians with deformations of the tangent bundle quantum sheaf cohomology is a 0 2 deformation of the ordinary quantum cohomology ring realized as the ope ring in a 2 twisted theories quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models glsms here we study 0 2 deformations of nonabelian glsms for which previous methods have been intractable combined with the classical result the quantum ring structure is derived from the one loop effective potential we also utilize recent advances in supersymmetric localization to compute a 2 correlation functions and check the general result in examples in this paper we focus on physics derivations and examples in a companion paper we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring