Tilting modules and the p-canonical basis - Archive ouverte HAL Access content directly
Journal Articles Asterisque Year : 2018

Tilting modules and the p-canonical basis

Abstract

In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block. Our conjecture implies character formulas for the simple and tilting modules in terms of the p-canonical basis, as well as a description of the principal block as the anti-spherical quotient of the Hecke category. We prove our conjecture for GLn using the theory of 2-Kac–Moody actions. Finally, we prove that the diagrammatic Hecke category of a general crystallographic Coxeter group may be described in terms of parity complexes on the flag variety of the corresponding Kac–Moody group.
Fichier principal
Vignette du fichier
tilting-total.pdf (1.16 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01249796 , version 1 (03-01-2016)
hal-01249796 , version 2 (14-01-2016)
hal-01249796 , version 3 (23-02-2017)

Identifiers

Cite

Simon Riche, Geordie Williamson. Tilting modules and the p-canonical basis. Asterisque, 2018, 397. ⟨hal-01249796v3⟩
404 View
689 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More