Some relative character theory
type: Item
instance of: scholarly article
title: Some relative character theory
zbMATH Open document ID: 0834.20006
DOI: 10.1016/0022-4049(93)00006-Q
author: Stephen Donkin
published in: Journal of Pure and Applied Algebra
publication date: 1996-03-06T00:00:00Z
review text: Let \(G\) be a finite group, \(H\) be a subgroup of \(G\) and \(A\) be the ring of integers of a number field \(K\). The main object of the paper is the \(A\)-algebra \(C_0(G,H)\) of \(H\)-class functions of \(G\). For a suitable cyclotomic field \(K\), \(C_0(G,H)\) contains an orthonormal basis. This is the main result of the paper. The well-known Brauer induction theorem is a consequence of this result. Earlier the author got the result in the case when \(G\) is the symmetric group and \(H\) is a Young subgroup.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C10
zbMATH DE Number: 735692
zbMATH Keywords: finite groups
zbMATH Keywords: number fields
zbMATH Keywords: class functions
zbMATH Keywords: cyclotomic fields
zbMATH Keywords: orthonormal bases
zbMATH Keywords: Brauer induction theorem
MaRDI profile type: Publication
cites work: Invariants of several matrices
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description: scientific article; zbMATH DE number 735692