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Tensor Square of the Minimal Representation of O(p, q)

Published online by Cambridge University Press:  20 November 2018

Alexander Dvorsky
Alexander Dvorsky*
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, FL 33124, U.S.A. e-mail: dvorsky@math.miami.edu
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Abstract

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In this paper, we study the tensor product $\pi ={{\sigma }^{\min }}\otimes {{\sigma }^{\min }}$ of the minimal representation ${{\sigma }^{\min }}$ of $O\left( p,q \right)$ with itself, and decompose $\pi$ into a direct integral of irreducible representations. The decomposition is given in terms of the Plancherel measure on a certain real hyperbolic space.

Keywords

22E46
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 1 , 01 March 2007 , pp. 48 - 55
Copyright
Copyright © Canadian Mathematical Society 2007

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