A new family of representations of virtually free groups

Abstract

We construct a new family of irreducible unitary representations of a finitely generated virtually free group Λ. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the regular representation, thus implying that all the representations in this family can be realized on the boundary of Λ. As a corollary, we obtain an analogue of Herz majorization principle.

Free group representations from vector-valued multiplicative functions, II

“…Since Γ acts amenably (in the sense of Zimmer) on Ω, a representation (π, H) of Γ admits a boundary realization if and only if it is tempered. This follows from the general considerations in [QS92]; a short proof specifically for the case at hand can be found in [IKS13].…”