Identities of Irreducible Representations and Gassmann Equivalence

Abstract

Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of identities related to spherical space forms and to representations of finite $p$-groups are presented. Some old results on irreducible representations with the same identities are revisited