Spherical varieties and langlands duality
WebThe spherical Hecke algebra for an arbitrary reductive group 56 5.2. Satake isomorphism 57 5.3. The Langlands correspondence for an arbitrary reductive group 59 ... the Langlands duality is indeed closely related to the S-duality of quantum eld theory, and this opens up exciting possibilities for both subjects. The goal of these notes is two ... WebNov 4, 2024 · To a spherical -variety , one associates a dual group and an -value (encoded in a representation of ), which conjecturally describe the local and automorphic spectra of the variety. This sets up a problem of functoriality, for any morphism of dual groups. We review, and generalize, Langlands' "beyond endoscopy" approach to this problem.
Spherical varieties and langlands duality
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WebIn an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at establishing their conjecture in the case of symmetric varieties (an important class of spherical varieties). A key ingredient is … WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space of X. The theory we develop …
WebELECTRO-MAGNETIC DUALITY AND GEOMETRIC LANGLANDS DUALITY 3 1.1.2. New perspectives. (1) Prediction of elements of the geometric Langlands program for surfaces. This is the most exciting aspect as mathematicians have not been making much progress on this question, at least until the recent work of Braverman and Finkel-berg. WebThe de nition of a spherical variety either asks for an open orbit for the Borel subgroup, or it has a multiplicity 1 property for algebraic representations. In the case of G=H, this asks for every irreducible to appear at least once. So this is a nice niteness condition. Examples of spherical varieties are given by the following.
WebToric and flag varieties are both examples of spherical varieties (as expected). Spherical varieties are intimately related to the Langlands program (both geometric and arithmetic). Executive summary: classically one studies automorphic forms on the upper half-plane by calculating period integrals. Now one would like to generalize this, and ... Webpaper studies the behavior of global Springer representations under Langlands duality. The main results in [Yun11] on which this paper relies will be reviewed in x1.3. 1.1 Motivations Let Gand G_be almost simple algebraic groups over an algebraic closed eld kwith dual root systems. We call them a pair of Langlands dual groups.
WebSpherical varieties and Langlands duality - CORE Reader
WebSpherical varieties are algebraic varieties equipped with an action of a certain type of algebraic group G subject to a finiteness condition. The type of G will be called reductive. … how to set chess pieces on boardWebSep 10, 2011 · We can view this isomorphism as a version of the geometric Langlands duality in the formal neighborhood of the trivial local system, for the group GL r . We … notcutts tunbridge wells opening timesWebquestion to purity of IC sheaves on affine flag varieties. Contents 1. Introduction. 2 1.1. Quantum groups, tilting modules and cohomology. 2 1.2. Koszul duality conjecture. 3 1.3. Plan of the paper. 4 1.4. Notations. 4 1.5. Acknowledgements 5 2. Coherent sheaves: exotic t-structure, and Positivity Lemma. 5 2.1. Exceptional sets and quasi ... how to set chime on pendulum clockWebTo an arbitrary affine spherical G-variety X, one may associate a horospherical variety Xhoro. Its associated subgroup Hˇhoro turns out to be a maximal torus in the subgroup Hˇ associated to X. 2000 Mathematics Subject Classification: 22E67, 14M17 Keywords and Phrases: Loop spaces, spherical varieties, Langlands duality how to set chrome as browserWebFrom two di erent sources, one expects a certain S-duality on the set of hyperspher-ical varieties (this duality acts on the groups involved as well). First, this comes from the S-duality of boundary conditions in N= 4 super Yang-Mills theory [10,11]. Second, this comes from the relative Langlands duality [2]; for a trailer see [1] or [3, §1.7]. how to set chinese typing input on windows 10WebMar 19, 2012 · We prove that the stable parts of the parabolic Hitchin complexes for Langlands dual group are naturally isomorphic after passing to the associated graded of … notcutts tunbridge wells jobsWebJan 24, 2004 · LANGLANDS DUALITY AND ALGEBRAIC GROUPS] 97 let Rep Gˇ k stand for the category of k-representations of Gˇ k; here Gˇ denotes the canonical smooth split reductive group scheme over k whose root datum is dual to that of G. The goal of this paper is to prove the following: (1.1) The categories PG O (Gr,k) and Rep Gˇ k are equivalent as … notcutts warrington