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Perverse sheaves on affine flags and langlands dual group

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Abstract

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].

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, Canada, M5S 2E4

    Sergey Arkhipov

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Roman Bezrukavnikov

Authors
  1. Sergey Arkhipov
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  2. Roman Bezrukavnikov
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Correspondence to Sergey Arkhipov.

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Arkhipov, S., Bezrukavnikov, R. Perverse sheaves on affine flags and langlands dual group. Isr. J. Math. 170, 135–183 (2009). https://doi.org/10.1007/s11856-009-0024-y

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  • DOI: https://doi.org/10.1007/s11856-009-0024-y

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