Exact values of Kazhdan constants for some finite groups
type: Item
instance of: scholarly article
title: Exact values of Kazhdan constants for some finite groups
zbMATH Open document ID: 0842.20013
author: Roland Bacher
author: Pierre de la Harpe
published in: Journal of Algebra
publication date: 1996-06-10T00:00:00Z
review text: Let \(\Gamma\) be a group generated by a finite set \(S\) and let \(k_\Gamma(S)=\inf\{k_\Gamma(S,\pi):\pi\) is a unitary representation with no nontrivial common fixed points\} \[ k_\Gamma(S,\pi)=\inf_{|x|=1}\max_{s\in S}|\pi(s)x-x|. \] The main result of the paper is the exact computation of \(k_\Gamma(S)\) for \(\Gamma=\sigma_n\), the symmetric group of \(n\) objects, and \(S\) a special set of transpositions. There are applications to finite graphs.
reviewed by: E.T.Ljubenova-Toneva
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 554218
zbMATH Keywords: unitary representations
zbMATH Keywords: Kazhdan constants
zbMATH Keywords: symmetric groups
zbMATH Keywords: transpositions
MaRDI profile type: Publication
full work available at URL: jabr.1994.1029
OpenAlex ID: W1987163543
DOI: 10.1006/JABR.1994.1029
description: scientific article; zbMATH DE number 554218