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Tilting modules and the p-canonical basis

Asterisque, 2018, Vol.397 [Peer Reviewed Journal]

Distributed under a Creative Commons Attribution 4.0 International License ;ISSN: 0303-1179 ;EISSN: 2492-5926 ;DOI: 10.24033/ast.1041

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  • Title:
    Tilting modules and the p-canonical basis
  • Author: Riche, Simon ; Williamson, Geordie
  • Subjects: Mathematics
  • Is Part Of: Asterisque, 2018, Vol.397
  • Description: 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.
  • Publisher: Société Mathématique de France
  • Language: English
  • Identifier: ISSN: 0303-1179
    EISSN: 2492-5926
    DOI: 10.24033/ast.1041
  • Source: Hyper Article en Ligne (HAL) (Open Access)
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