Spherical functions and uniformly bounded representations of free groups

Volume 100 / 1991

Tadeusz Pytlik Studia Mathematica 100 (1991), 237-250 DOI: 10.4064/sm-100-3-237-250


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.


  • Tadeusz Pytlik

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