Smith-Treumann theory and the linkage principle
Representation Theory
2022-05-16 v2 Algebraic Geometry
Algebraic Topology
Abstract
We apply Treumann's "Smith theory for sheaves" in the context of the Iwahori--Whittaker model of the Satake category. We deduce two results in the representation theory of reductive algebraic groups over fields of positive characteristic: (a) a geometric proof of the linkage principle; (b) a character formula for tilting modules in terms of the -canonical basis, valid in all blocks and in all characteristics.
Cite
@article{arxiv.2003.08522,
title = {Smith-Treumann theory and the linkage principle},
author = {Simon Riche and Geordie Williamson},
journal= {arXiv preprint arXiv:2003.08522},
year = {2022}
}
Comments
52 pages, revised version, to appear in Publ. IHES