Free group representations from vector-valued multiplicative functions, II

Let Γ 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 Γ and proved them irreducible as representation of Γ ⋠λC(Ω). In this paper we analyze multiplicative representations as representations of Γ and we prove a criterium for irreducibility based on the growth of their matrix coefficients.