A new family of representatiosnof virtually free groups

TL;DR

This paper introduces a novel family of irreducible unitary representations for finitely generated virtually free groups, extending understanding of their boundary representations and related harmonic analysis principles.

Contribution

It constructs a new family of representations and proves a general result linking hyperbolic group representations to boundary realizations, advancing the theory of group representations.

Findings

New family of irreducible unitary representations constructed

Representation boundary realization established for hyperbolic groups

Herz majorization principle analogue derived

Abstract

We construct a new family of irreducible unitary representations of a finitely generated virtually free group L. 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 L. As a corollary, we obtain an analogue of Herz majorization principle.