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Smith-Treumann theory and the linkage principle

By Simon Riche and Geordie Williamson

Abstract

In this paper 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 p-canonical basis, valid in all blocks and in all characteristics

Topics: [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]
Publisher: HAL CCSD
Year: 2020
OAI identifier: oai:HAL:hal-02570416v1
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