Modular affine Hecke category and regular centralizer

Roman Bezrukavnikov (1) , Simon Riche (2, 3)

1 Department of Mathematics [MIT]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 UCA - Université Clermont Auvergne

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.

Domains: Representation Theory [math.RT]

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