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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Donald I. Cartwright, Gabriella Kuhn and Paolo M. Soardi
Journal: Trans. Amer. Math. Soc. 353 (2001), 349-364
MSC (2000): Primary 20E08, 20C15; Secondary 22E40
Published electronically: September 18, 2000
MathSciNet review: 1707193
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Abstract:

Let $G=\mathrm{Aut}(T)$ be the group of automorphisms of a homogeneous tree $T$, and let $\Gamma$ be a lattice subgroup of $G$. Let $\pi$ be the tensor product of two spherical irreducible unitary representations of $G$. We give an explicit decomposition of the restriction of $\pi$ to $\Gamma$. We also describe the spherical component of $\pi$ explicitly, and this decomposition is interpreted as a multiplication formula for associated orthogonal polynomials.


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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@matapp.unimib.it

Paolo M. Soardi
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Viale Sarca 202, Edificio U7, 20126 Milano, Italy
Email: soardi@matapp.unimib.it

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02584-8
PII: S 0002-9947(00)02584-8
Keywords: Spherical representation, homogeneous tree
Received by editor(s): January 22, 1996
Received by editor(s) in revised form: April 23, 1999
Published electronically: September 18, 2000
Article copyright: © Copyright 2000 American Mathematical Society