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

Published:2007-03-01
Printed: Mar 2007
• Alexander Dvorsky
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## Abstract

In this paper, we study the tensor product $\pi=\sigma^{\min}\otimes \sigma^{\min}$ of the minimal representation $\sigma^{\min}$ of $O(p,q)$ 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.
 MSC Classifications: 22e46 - unknown classification 22e46