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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 $Γ\ltimes_λC(Ω)$. 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.