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Tensor Square of the Minimal Representation of O(p, q)
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2007
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