Free group representations from vector-valued multiplicative functions, II

Abstract

Let \(\Gamma \) be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of \(\Gamma \) and proved them irreducible as representation of \(\Gamma \ltimes _\lambda C(\Omega )\). In this paper we analyze multiplicative representations as representations of \(\Gamma \) and we prove a criterium for irreducibility based on the growth of their matrix coefficients.