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Perverse sheaves on affine flags and Langlands dual group

Sergey Arkhipov·Roman Bezrukavnikov
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Abstract

The geometric Satake isomorphism is an equivalence between the categories of spherical perverse sheaves on affine Grassmanian and the category of representations of the Langlands dual group. We provide a similar description for derived categories of l-adic sheaves on an affine flag variety which are geometric counterparts of a maximal commutative subalgebra in the Iwahori Hecke algebra; of the anti-spherical module over this algebra; and of the space of Iwahori-invariant Whitakker functions.

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BibTeXRIS

Sergey Arkhipov, Roman Bezrukavnikov. 2002-01-09. Perverse sheaves on affine flags and Langlands dual group. https://arxiv.org/abs/math/0201073

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