Brauer morphism between modular Hecke algebras
type: Item
instance of: scholarly article
title: Brauer morphism between modular Hecke algebras
zbMATH Open document ID: 0656.20003
DOI: 10.1016/0021-8693(88)90280-3
author: Marc Cabanes
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let k be an algebraically closed field of prime characteristic p, let G be a finite group, and let M be a kG-module. For any p-subgroup Q of G, one has a \(kN_ G(Q)/Q\)-module M(Q) and a Brauer morphism \(Br_ Q: M^ Q\to M(Q)\). If M is a p-permutation module (also called a trivial source module) then \((End_ k(M))(Q)\) and \(End_ k(M(Q))\) are isomorphic so one obtains a Brauer morphism \(End_{kQ}(M)\to End_ k(M(Q))\). This Brauer morphism is studied in the case where G is a finite group with split BN-pair in characteristic p, \(U=O_ p(B)\), \(M=Ind^ G_ U(k)\), P is a parabolic subgroup of G and \(Q=O_ p(P)\); in this case \(N_ G(Q)/Q\) is isomorphic to a Levi subgroup of G. Along the way the author presents a more or less self-contained introduction into the representation theory of G (as developed by Curtis, Richen, Sawada, Green, Tinberg) simplifying proofs of some of the known results. One of the applications is the verification of Alperin's weight conjecture for finite groups with split BN-pair in characteristic p.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 4071167
zbMATH Keywords: Green correspondence
zbMATH Keywords: vertex
zbMATH Keywords: Hecke algebra
zbMATH Keywords: kG-module
zbMATH Keywords: p-subgroup
zbMATH Keywords: p- permutation module
zbMATH Keywords: trivial source module
zbMATH Keywords: Brauer morphism
zbMATH Keywords: finite group with split BN-pair
zbMATH Keywords: Levi subgroup
zbMATH Keywords: Alperin's weight conjecture
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90280-3
OpenAlex ID: W2022540711
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description: scientific article; zbMATH DE number 4071167