Tilting modules and the p-canonical basis / Simon Riche & Geordie Williamson.

Format:

Book

Author/Creator:

Riche, Simon, 1982- author.

Williamson, Geordie, 1981- author.

Series:

Astérisque ; 397.

Astérisque, 0303-1179 ; 397

Language:

English

French

Subjects (All):

Linear algebraic groups.

Geometry, Algebraic.

Representations of algebras.

Hecke algebras.

Weyl groups.

Kac-Moody algebras.

Physical Description:

ix, 184 pages : illustrations ; 24 cm.

Place of Publication:

Paris : Société mathématique de France, 2018.

Language Note:

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

Summary:

"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).

ISBN:

9782856298800

285629880X

OCLC:

1038535853