A product formula for spherical representations of a group of automorphisms of a homogeneous tree, II

Authors:
Donald I. Cartwright and Gabriella Kuhn

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2073-2090

MSC (2000):
Primary 20E08, 20C15; Secondary 20C30

DOI:
https://doi.org/10.1090/S0002-9947-00-02757-4

Published electronically:
December 29, 2000

MathSciNet review:
1813608

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Abstract | References | Similar Articles | Additional Information

Let be the group of automorphisms of a homogeneous tree and let be the tensor product of two spherical irreducible unitary representations of . We complete the explicit decomposition of commenced in part I of this paper, by describing the discrete series representations of which appear as subrepresentations of .

**1.**D.I. Cartwright, G. Kuhn and P.M. Soardi,*A product formula for spherical representations of a group of automorphisms of a homogeneous tree, I*, Trans. Amer. Math. Soc.**353**, 2000, 349-364. CMP**99:17****2.**A. Figà-Talamanca and C. Nebbia,*Harmonic analysis and representation theory for groups acting on homogeneous trees*, London Mathematical Society Lecture Note Series**162**, Cambridge University Press, Cambridge, 1991. MR**93f:22004****3.**G. James and A. Kerber,*The representation theory of the symmetric group*, Encyclopedia of mathematics and its applications, Volume 16, Addison-Wesley Publishing Company, 1981. MR**83k:20003****4.**G.I. Olshanskii,*Classification of irreducible representations of groups of automorphisms of Bruhat-Tits trees*, Functional Anal. Appl.,**11**, 1977, 26-34.**5.**J. Repka,*Tensor products of unitary representations of*, Amer. J. Math.,**100**, 1978, 747-774. MR**80g:22014**

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Additional Information

**Donald I. Cartwright**

Affiliation:
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia

Email:
donaldc@maths.usyd.edu.au

**Gabriella Kuhn**

Affiliation:
Dipartimento di matematica e applicazioni, Università di Milano-Bicocca, Viale Sarca 202, Edificio U7, 20126 Milano, Italy

Email:
kuhn@vmimat.mat.unimi.it

DOI:
https://doi.org/10.1090/S0002-9947-00-02757-4

Keywords:
Homogeneous tree,
spherical representation

Received by editor(s):
February 8, 2000

Published electronically:
December 29, 2000

Article copyright:
© Copyright 2000
American Mathematical Society