Multiplicity one theorems: the Archimedean case
Abstract
Let G be one of the classical Lie groups n+1(), n+1(), (p,q+1), (p,q+1), n+1(), (p,q+1), n+1(), and let G' be respectively the subgroup n(), n(), (p,q), (p,q), n(), (p,q), n(), embedded in G in the standard way. We show that every irreducible Casselman-Wallach representation of G' occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of G. Similar results are proved for the Jacobi groups n() 2n+1(), n() 2n+1(), (p,q) 2p+2q+1(), 2n() 2n+1(), 2n() 2n+1(), with their respective subgroups n(), n(), (p,q), 2n(), 2n().
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