Spherical distribution vectors

Abstract

In this paper we consider a locally compact second countable unimodular group $G$ and a closed unimodular subgroup $H$. Let $\rho$ be a finite dimensional unitary representation of $H$ with closed image. For the unitary representation of $G$ obtained by inducing $\rho$ from $H$ to $G$ a decomposition in Hilbert subspaces of a certain space of distributions is given. It is shown that the representations relevant for this decomposition are determined by so-called $(\rho,H)$ spherical distributions, which leads to a description of the decomposition on the level of these distributions. \u