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, and the second step in our project towards the construction of an equivalence of categories relating the two natural geometric realizations of the associated affine Hecke algebra in the case of positive-characteristic coefficients.
Cite
@article{arxiv.2206.03738,
title = {Modular affine Hecke category and regular centralizer},
author = {Roman Bezrukavnikov and Simon Riche},
journal= {arXiv preprint arXiv:2206.03738},
year = {2024}
}
Comments
v1: 164 pages, this paper is a sequel to arXiv:2005.05583 (whose title will be updated); v2: 148 pages, minor revision, some changes of notation for consistency with later paper arXiv:2402.08281, removed Section 13 (which will be treated in a separate paper)