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 $\Pi|_{G'}$ with respect to the pair $(G,G')=(O(p,q), O(p',q') \times O(p'',q''))$ for irreducible unitary representations $\Pi$ of $G$ that are "geometric quantization" of minimal elliptic coadjoint orbits. We also construct explicitly all holographic operators and prove a closed Parseval-type formula.