Bessel functions on finite groups
type: Item
instance of: scholarly article
title: Bessel functions on finite groups
zbMATH Open document ID: 0831.20007
author: J. L. Alperin
author: Gordon James
published in: Journal of Algebra
publication date: 1996-02-06T00:00:00Z
review text: Let \(U\), \(K\), \(G\) be finite groups, \(U\subseteq K\subseteq G\), \(\vartheta\) a linear character of \(U\), \(e_\vartheta=\vartheta(1)|U|^{-1}\sum \vartheta(u^{-1})u\) the corresponding primitive central idempotent, and let \(\psi\) be an irreducible character of \(G\). The corresponding Bessel function \(J\) on \(G\) is defined by \(J(g)=\psi (ge_\vartheta)\) and is equal to \(J(g)=|U|^{-1} \sum_u \vartheta (u^{-1}) \psi (gu)\). The authors prove the following Theorem: Let \(\varphi\) be an irreducible character of \(K\) which is induced by \(\vartheta\) and assume the restriction of \(\psi\) to \(K\) is \(\varphi\), i.e., \(\vartheta^K=\varphi=\psi_K\). Furthermore let \(g_1, \dots, g_r\) be a complete set of right coset representatives for \(U\) in \(K\) and for each \(g \in G\) define the matrix \(M(g)=(J(g_i gg^{-1}_j))\). Then \(M\) is a representation of \(G\) with character \(\psi\).
reviewed by: B.G.Basmaji
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 735314
zbMATH Keywords: finite groups
zbMATH Keywords: linear characters
zbMATH Keywords: primitive central idempotents
zbMATH Keywords: irreducible characters
zbMATH Keywords: Bessel functions
MaRDI profile type: Publication
full work available at URL: jabr.1995.1025
OpenAlex ID: W2075330676
DOI: 10.1006/JABR.1995.1025
description: scientific article; zbMATH DE number 735314