Remote Access Transactions of the American Mathematical Society
Green Open Access

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, 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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

Let $G=\text{Aut}(T)$ be the group of automorphisms of a homogeneous tree $T$and let $\pi$ be the tensor product of two spherical irreducible unitary representations of $G$. We complete the explicit decomposition of $\pi$commenced in part I of this paper, by describing the discrete series representations of $G$ which appear as subrepresentations of $\pi$.


References [Enhancements On Off] (What's this?)

  • 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 $SL_2(\mathbb{R} )$, Amer. J. Math., 100, 1978, 747-774. MR 80g:22014

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20E08, 20C15, 20C30

Retrieve articles in all journals with MSC (2000): 20E08, 20C15, 20C30


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

American Mathematical Society