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Perverse sheaves on affine flags and nilpotent cone of the langlands dual group

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Abstract

This paper is a continuation of [2]. In [2], we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) a category of constructible sheaves on the affine flag variety of the Langlands dual group. Below we prove certain properties of this equivalence related to cells in the affineWeyl group; provide a similar “Langlands dual” description for the category of equivariant coherent sheaves on the nilpotent cone, and link it to perverse coherent sheaves; and deduce some conjectures by Lusztig and Ostrik.

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

    Roman Bezrukavnikov

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  1. Roman Bezrukavnikov
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Correspondence to Roman Bezrukavnikov.

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Bezrukavnikov, R. Perverse sheaves on affine flags and nilpotent cone of the langlands dual group. Isr. J. Math. 170, 185–206 (2009). https://doi.org/10.1007/s11856-009-0025-x

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  • DOI: https://doi.org/10.1007/s11856-009-0025-x

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