Identities of Irreducible Representations and Gassmann Equivalence

TL;DR

This paper explores how identities derived from character values of complex irreducible representations of finite groups can determine representations up to Gassmann equivalence, with applications to spherical space forms and p-groups.

Contribution

It provides explicit constructions of identities from character sets and revisits classical results on representations sharing the same identities.

Findings

Identities can determine representations up to Gassmann equivalence

Examples include spherical space forms and finite p-groups

Old results on irreducible representations with identical identities are revisited

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