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.
