Tensor product decomposition for rank-one spin groups I : unitary principal series representations

Abstract

We provide an explicit direct integral decomposition for the tensor product representation $\pi_1\widehat{\otimes}\pi_2$ of the rank one spin group $\mathrm{Spin}(n,1)$ whenever $\pi_1$ is a unitary principal series representation and $\pi_2$ is an arbitrary irreducible unitary representation of $\mathrm{Spin}(n,1)$.