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  3. Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees
  • Cited by 62
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1991
Online ISBN:
9780511662324
DOI:
https://doi.org/10.1017/CBO9780511662324
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Algebra
Series:
London Mathematical Society Lecture Note Series (162)
Information

Book 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'shiankii. 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.

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