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 $\Pi {|}_{G^{\prime }}$ with respect to the pair $(G,G^{\prime })=(O(p,q),O(p^{\prime },q^{\prime })\times O(p^{\prime \prime },q^{\prime \prime }))$ 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.

To appear in Adv Math

References in corpus (3)

• Branching Laws for Some Unitary Representations of SL(4,R)
• Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad
• Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability

Cited by in corpus (7)

• Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability
• Conjectures on reductive homogeneous spaces
• Bounded multiplicity theorems for induction and restriction
• Multiplicity in restricting minimal representations
• A hidden symmetry of a branching law
• Branching of unitary $O(1,n+1)$-representations with non-trivial $(\mathfrak{g},K)$-cohomology
• Recent advances in branching problems of representations