Construction of central elements in the affine Hecke algebra via nearby cycles
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In this paper, a connected reductive group over a finite field Fq and a corresponding group over the local field K = Fq((t)) is defined, where Hsph as a vector space consists of compactly supported bi-G(O)invariant functions G(K) → Q and the product is defined byAbstract:
0.1. Overview. Let G be a connected reductive group over a finite field Fq and let G(K) be the corresponding group over the local field K = Fq((t)). Let G(O) ⊂ G(K) be a maximal compact subgroup of G(K) (here O = Fq[[t]]) and let Hsph denote the Hecke algebra of G(K) with respect to G(O). In other words, Hsph as a vector space consists of compactly supported bi–G(O)–invariant functions G(K) → Q and the product is defined byread more
Citations
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Gauge Theory, Ramification, And The Geometric Langlands Program
Sergei Gukov,Edward Witten +1 more
TL;DR: In this paper, the authors show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification, which involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification.
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Twisted loop groups and their affine flag varieties
Georgios Pappas,Michael Rapoport +1 more
TL;DR: In this article, a theory of affine flag varieties and Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field was developed.
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The decomposition theorem, perverse sheaves and the topology of algebraic maps
Mark Andrea,Luca Migliorini +1 more
TL;DR: In this paper, a survey of the theory of perverse sheaves is presented, concluding with the decomposition theorem of Beilinson, Bernstein, Deligne, and Gabber.
Journal ArticleDOI
Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale
TL;DR: For any reductive group G over a global function field, the authors used the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the direction from automorphic to Galois.
Book ChapterDOI
Local geometric Langlands correspondence and affine Kac-Moody algebras
Edward Frenkel,Dennis Gaitsgory +1 more
TL;DR: In this article, the affine Kac-Moody algebra is used to define representations of critical level on twisted D-modules on the quotient of the loop group G((t)) by its open compact subgroup K, such as the Iwahori subgroup I.
References
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Joseph Bernstein,Valery A. Lunts +1 more
TL;DR: In this paper, the DG-modules and equivariant cohomology of toric varieties have been studied, and the derived category D G (X) and functors have been defined.
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Arnaud Beauville,Y. Laszlo +1 more
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V. G. Drinfeld,Carlos Simpson +1 more
TL;DR: Theorem 1.1 as mentioned in this paper shows that for any algebraically closed field k there is a bijection G → G ⊗ k between isomorphism classes of such group schemes and isomorphisms classes of connected reductive algebraic groups over k.
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How to glue perverse sheaves
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