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

## TL;DR

This paper provides a comprehensive analysis of how certain unitary representations of indefinite orthogonal groups decompose when restricted to specific subgroups, including explicit constructions and formulas.

## Contribution

It offers a complete description of the discrete spectra in the branching laws for representations associated with minimal elliptic orbits, including explicit holographic operators and a Parseval-type formula.

## Key findings

- Complete description of discrete spectra in branching laws
- Explicit construction of holographic operators
- Proof of a closed Parseval-type formula

## 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.