Positive definite functions of finitary isometry groups over fields of odd characteristic.
type: Item
instance of: scholarly article
title: Positive definite functions of finitary isometry groups over fields of odd characteristic.
zbMATH Open document ID: 1116.20003
author: Felix Leinen
author: Orazio Puglisi
published in: Journal of Pure and Applied Algebra
publication date: 2007-01-09T00:00:00Z
review text: A group is said to be finitary linear if it acts faithfully on a vector space such that the fixed-point space of every element of the group has finite codimension in the vector space. Let \(G\) be a group. A normalized positive definite \(\mathbb{C}\)-linear class function is a function \(f\colon\mathbb{C} G\to\mathbb{C}\) such that \(f(1)=1\) and \(f(x^*x)\geq 0\) for all \(x\in\mathbb{C} G\), where * denotes a certain anti-automorphism of \(\mathbb{C} G\). Extremal positive definite class functions can be considered as generalized irreducible characters. The authors investigate finitary classical groups over finite fields of odd characteristic. They give a classification of extremal positive definite class functions for the orthogonal group, the unitary group, and the symplectic group.
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 42A82
zbMATH DE Number: 5083177
zbMATH Keywords: positive definite functions
zbMATH Keywords: finitary isometry groups
zbMATH Keywords: orthogonal groups
zbMATH Keywords: unitary groups
zbMATH Keywords: symplectic groups
zbMATH Keywords: complex group algebras
zbMATH Keywords: simple locally finite groups
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: j.jpaa.2006.05.007
OpenAlex ID: W2146569801
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DOI: 10.1016/J.JPAA.2006.05.007
description: scientific article; zbMATH DE number 5083177