Harmonic analysis and representation theory for groups acting on homogeneous trees. (English) Zbl 1154.22301
London Mathematical Society Lecture Note Series 162. Cambridge etc.: Cambridge University Press (ISBN 0-521-42444-5). ix, 151 p. (1991).
Publisher’s description: These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G. I. Ol’shanskiĭ. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.
MSC:
22D12 | Other representations of locally compact groups |
22-02 | Research exposition (monographs, survey articles) pertaining to topological groups |
43-02 | Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis |
20E08 | Groups acting on trees |
22E50 | Representations of Lie and linear algebraic groups over local fields |
43A85 | Harmonic analysis on homogeneous spaces |
43A90 | Harmonic analysis and spherical functions |
57M07 | Topological methods in group theory |