Smith-Treumann theory and the linkage principle

Simon Riche (1, 2) , Geordie Williamson (3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
3 The University of Sydney

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.

Domaines: Théorie des représentations [math.RT]

Simon Riche, Geordie Williamson. Smith-Treumann theory and the linkage principle. Publications mathematiques de l' IHES, 2022, 136, pp.225-292. ⟨hal-02570416⟩