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Preprints, Working Papers, ... Year : 2022

Modular affine Hecke category and regular centralizer

Abstract

In this paper we provide a "combinatorial" description of the category of tilting perverse sheaves on the affine flag variety of a reductive algebraic group, and its free-monodromic variant, with coefficients in a field of positive characteristic. This provides a replacement for the familiar "Soergel theory" for characteristic-0 coefficients. As an application we deduce character formulas for indecomposable tilting perverse sheaves on the affine flag variety in terms of l-Kazhdan-Lusztig polynomials.
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Dates and versions

hal-03691331 , version 1 (09-06-2022)

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Roman Bezrukavnikov, Simon Riche. Modular affine Hecke category and regular centralizer. 2022. ⟨hal-03691331⟩
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