Bounded Multiplicity Branching for Symmetric Pairs

We prove that any simply connected non-compact semisimple Lie group G admits an infinite-dimensional irreducible representation p with bounded multiplicity property of the restriction p|(G'') for all symmetric pairs (G, G''). We also discuss which irreducible representations p satisfy the bounded multiplicity property. Mathematics Subject Classification: Primary 22E46; secondary 22E45, 53C35, 32M15, 53C15.