Perverse sheaves on affine flags and langlands dual group
نویسندگان
چکیده
منابع مشابه
Perverse Sheaves on Affine Flags and Langlands Dual Group
This is the first in a series of papers devoted to describing the category of sheaves on the affine flag manifold of a (split) simple group in terms 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...
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In this paper we outline a proof of a geometric version of the Satake isomorphism. Namely, given a connected, complex algebraic reductive group G we show that the tensor category of representations of the dual group G is naturally equivalent to a certain category of perverse sheaves on the affine Grassmannian of G. This can be extended to give a topological realization of algebraic representati...
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on the set of F-rational points of X given by the alternating sum of traces of Fr, the Frobenius action on stalks of the cohomology sheaves HiF . He then went on to initiate an ambitious program of giving geometric (= sheaf theoretic) meaning to various classical algebraic formulas via the above “functions-faisceaux” correspondence F 7→ χ F . This program got a new impetus with the discovery of...
متن کاملPerverse Sheaves on Grassmannians
We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.
متن کاملNotes on Perverse Sheaves and Intersection
Unless specified otherwise, by “manifolds” and “varieties” we shall always mean, respectively, complex manifolds and complex algebraic varieties. Consequently, “dimension” (of a manifold or variety) always refers to the complex dimension. We also fix, once and for all, a commutative Noetherian ring k of finite global dimension as our ring of “coefficients”; the reader is welcome to take k = Z,Q...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2009
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-009-0024-y