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A product formula for spherical representations of a group of automorphisms of a homogeneous tree, II
Author(s):
Donald
I.
Cartwright;
Gabriella
Kuhn
Journal:
Trans. Amer. Math. Soc.
353
(2001),
2073-2090.
MSC (2000):
Primary 20E08, 20C15;
Secondary 20C30
Posted:
December 29, 2000
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Abstract:
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 .
References:
-
- 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:
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
Posted:
December 29, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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