Spherical functions and uniformly bounded representations of free groups
Volume 100 / 1991
Studia Mathematica 100 (1991), 237-250
DOI: 10.4064/sm-100-3-237-250
Abstract
We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.