Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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, II


Authors: Donald I. Cartwright and Gabriella Kuhn
Journal: Trans. Amer. Math. Soc. 353 (2001), 2073-2090
MSC (2000): Primary 20E08, 20C15; Secondary 20C30
Published electronically: December 29, 2000
MathSciNet review: 1813608
Full-text PDF Free Access

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. Alessandro Figà-Talamanca and Claudio Nebbia, Harmonic analysis and representation theory for groups acting on homogeneous trees, London Mathematical Society Lecture Note Series, vol. 162, Cambridge University Press, Cambridge, 1991. MR 1152801 (93f:22004)
  • 3. Gordon James and Adalbert Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981. With a foreword by P. M. Cohn; With an introduction by Gilbert de B. Robinson. MR 644144 (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. Joe Repka, Tensor products of unitary representations of 𝑆𝐿₂(𝑅), Amer. J. Math. 100 (1978), no. 4, 747–774. MR 509073 (80g:22014), http://dx.doi.org/10.2307/2373909

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: http://dx.doi.org/10.1090/S0002-9947-00-02757-4
PII: S 0002-9947(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