A reciprocal branching problem for automorphic representations and global Vogan packets

Abstract

Let $G$ be a group and $H$ be a subgroup of $G$. The classical branching rule (or symmetry breaking) asks: For an irreducible representation $\pi$ of $G$, determine the occurrence of an irreducible representation $\sigma$ of $H$ in the restriction of $\pi$ to $H$. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation $\sigma$ of $H$, find an irreducible representation $\pi$ of $G$ such that $\sigma$ occurs in the restriction of $\pi$ to $H$. For automorphic representations of classical groups, the branching problem has been addressed by the well-known global Gan-Gross-Prasad conjecture. In this paper, we investigate the reciprocal branching problem for automorphic representations of special orthogonal groups using the twisted automorphic descent method as developed in [JZ15]. The method may be applied to other classical groups as well.

arXiv commentComments are welcome

References in corpus (4)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux
• La conjecture locale de Gross-Prasad pour les groupes spéciaux orthogonaux: le cas général
• Arthur Parameters and Cuspidal Automorphic Modules of Classical Groups