Exact values of kazhdan constants for some finite groups

Abstract

We compute exact values of numerical constants attached to finite groups given together with sets of generators. The definitions of these constants are suggested by Kazhdan’s work on unitary representations and his “Property (T).” Our main result is about symmetric groups, and its proof involves an analysis of Young’s standard representations. There is an appendix giving consequences of our result for finite graphs. 1994 Academic Press, Inc.