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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A product formula for spherical representations of a group of automorphisms of a homogeneous tree, I
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by Donald I. Cartwright, Gabriella Kuhn and Paolo M. Soardi PDF
Trans. Amer. Math. Soc. 353 (2001), 349-364 Request permission

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
  • MR Author ID: 45810
  • 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
  • Received by editor(s): January 22, 1996
  • Received by editor(s) in revised form: April 23, 1999
  • Published electronically: September 18, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 349-364
  • MSC (2000): Primary 20E08, 20C15; Secondary 22E40
  • DOI: https://doi.org/10.1090/S0002-9947-00-02584-8
  • MathSciNet review: 1707193