Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q)

Abstract

We give a complete description of the discrete spectra in the branching law Π|G′ with respect to the pair (G,G′)=(O(p,q),O(p′,q′)×O(p″,q″)) for irreducible unitary representations Π of G that are ‘‘geometric quantization’’ of minimal elliptic coadjoint orbits. We also construct explicitly all holographic operators and prove a Parseval-type formula.