ArticleOriginal scientific text
Title
Spherical functions and uniformly bounded representations of free groups
Authors 1
Affiliations
- Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
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.
Keywords
free group, uniformly bounded representation, spherical functions
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Pages:
237-250
Main language of publication
English
Received
1991-01-10
Published
1991
Exact and natural sciences