More irreducible boundary representations of free groups (Q1919631)

We construct a new class of irreducible unitary representations of free groups. These representations are weakly contained in the regular representation and are realized on the boundary. They are the generic elements of a family of representations which includes the spherical series, but their behavior is different from that of the spherical series representations. Specifically, they have one, not two boundary realizations, and their matrix coefficient functions are larger. In the appendix there is a short proof that all boundary representations of the free group are weakly contained in the regular representation.