Tilting modules and the p-canonical basis
By: Simon Riche & Geordie Williamson
Contributors: Williamson, Geordie, 1981- author
Series: Astérisque -- 397; Astérisque -- 397.
Publisher: Société mathématique de France
Published: 2018
Place of publication: Paris
Language: eng
Number of pages: 184
ISBN-13: 9782856298800
Subjects: Linear algebraic groups; Algebraic Geometry; Representations of algebras; Hecke algebras; Weyl groups; Kac-Moody algebras; 31.21 theory of groups
Description: "In this book 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 antispherical quotient of the Hecke category. We prove our conjecture for GL_n(K) 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."--Back cover
Notes: Includes bibliographical references (pages 179-184).

Text in in English; abstract is in English and French.