Spherical distribution vectors (Q1862239)

Let \(G\) be a locally compact second countable unimodular group and let \(H\) be its closed unimodular subgroup. For the unitary representation of \(G\) obtained by inducing a finite dimensional unitary representation \(\rho\) of \(H\) with closed image, 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. This leads to a description of the decomposition on the level of these distributions.