A hidden symmetry of a branching law

Abstract

We consider branching laws for the restriction of some irreducible unitary representations $\Pi$ of $G=O(p,q)$ to its subgroup $H=O(p-1,q)$. In Kobayashi (arXiv:1907.07994), the irreducible subrepresentations of $O(p-1,q)$ in the restriction of the unitary $\Pi {|}_{O(p-1,q)}$ are determined. By considering the restriction of packets of irreducible representations we obtain another very simple branching law, which was conjectured in Orsted-Speh (arXiv:1907.07544).

16 pages

References in corpus (1)

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