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Spherical functions on symmetric graphs. (English) Zbl 0535.43005
Harmonic analysis, Proc. Conf., Cortona/Italy 1982, Lect. Notes Math. 992, 342-386 (1983).
[For the entire collection see Zbl 0504.00013.]
The theory of representations of free groups with finitely many generators has been recently considered in analogy with the semisimple theory. This analogy arises from the realization of a free group as a homogeneous tree playing the role of the symmetric space G/K for a semisimple Lie group G with maximal compact subgroup K, and relies upon the use of the Poisson boundary and spherical functions. The use of spherical functions on free groups has been extended to every group acting isometrically and simply transitively on a homogeneous tree. The aim of this paper is to establish a similar theory for groups acting on suitable graphs.
Reviewer: B.Basit

MSC:
43A85 Harmonic analysis on homogeneous spaces
20E05 Free nonabelian groups
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
43A90 Harmonic analysis and spherical functions