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arXiv:math/0201073 [math.RT]AbstractReferencesReviewsResources

Perverse sheaves on affine flags and Langlands dual group

Sergey Arkhipov, Roman Bezrukavnikov

Published 2002-01-09, updated 2020-02-11Version 6

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.

Comments: 32 pages; some corrections, epigraph added. See arXiv:1807.07614 for corrected proof of Lemma 5
Categories: math.RT, math.AG
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