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.
@article{bwmeta1.element.bwnjournal-article-smv100i3p237bwm,
author = {Tadeusz Pytlik},
title = {Spherical functions and uniformly bounded representations of free groups},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {237-250},
zbl = {0754.22002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i3p237bwm}
}
Pytlik, Tadeusz. Spherical functions and uniformly bounded representations of free groups. Studia Mathematica, Tome 100 (1991) pp. 237-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i3p237bwm/
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