Multiplicity free subgroups of semi-direct products (Q1042753)

Let \(G\) be a locally compact unimodular group and \(H\) a compact subgroup. The pair \((G,H)\) is called multiplicity free if every irreducible unitary representation of \(G,\) when restricted to \(H,\) decomposes multiplicity free into irreducible unitary representations of \(H.\) It is shown that this condition is equivalent to the pair \((G \times H, \) diag\((H \times H)) \) being a Gelfand pair. More general definitions are given and results obtained for the case when \(H\) is not compact.