Separation of unitary representations of certain Cartan motion groups

Abstract

Let G be a connected semisimple Lie group with nite center, K a maximal compact connected subgroup of G and G0 the Cartan motion group associated to the Riemannian symmetric pair (G;K). Under two assumptions on the pair (G;K), we show that every irreducible unitary representation of G0 is characterized by a single element in its generalized moment set.