Perverse sheaves on affine flags and langlands dual group

By Sergey V. Arkhipov, R. Bezrukavnikov. 2002

118 citations recorded by the source corpus.

This is the first in a series of papers devoted to describing the category of sheaves on the affine flag manifold of a simple algebraic group in terms of the Langlands dual group. In the present paper we provide such a description for categories which are geometric counterparts of a maximal commutative subalgebra in the Iwahori Hecke algebra ℍ; of the anti-spherical module for ℍ; and of the space of Iwahori-invariant Whittaker functions. As a byproduct we obtain some new properties of central sheaves introduced in [G].

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/abd20431a4891e21a331c431c5716390bea364c2

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Citations in the corpus

Quantum groups, the loop Grassmannian, and the Springer resolution (2003, background): “N. Moreover, an additional argument based on results of [ AB ] shows that the parameters labelling the tilting objects in block(U) and the simple perverse coherent sheaves on e”
Whittaker functions and Demazure operators (2011, background): “Closely related facts may be found in Arkhipov and Bezrukavnikov [2] and Reeder [27].”
On two geometric realizations of an affine Hecke algebra (2012, methodology): “A step in this direction has been made in the previous works [1], [12], where a geometric theory of the anti-spherical (Whittaker) module over H was developed;(1) in the present paper we extend this analysis to the affine Hecke algebra itself.”
Perverse sheaves on affine flags and nilpotent cone of the langlands dual group (2002, unknown): “It was shown in [1] that the map V ⊗ O 7→ Z(V ) extends naturally to a monoidal functor Coh fr (N) → DI(Fl); we denote the resulting monoidal functor by Z̃ (thus Z̃ = F ◦ pSpr in notations of [1]).”
Local geometric Langlands correspondence and affine Kac-Moody algebras (2005, background): “According to [ AB ], the triangulated category Db(D(FlG)–mod) is a category over the stack e”
Kloosterman sheaves for reductive groups (2010, background): “HkV (A)|BunG(0,2)×X = A γ E V , where E V [1] is a perverse sheaf on X.”
Local models of Shimura varieties and a conjecture of Kottwitz (2011, unknown): “[2, 77]).”