## Abstract

Let G be a group and let H be a subgroup of G. The classical branching rule (or symmetry breaking) asks: For an irreducible representation πof G, determine the occurrence of an irreducible representation σ of H in the restriction of πto H. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation σ of H, find an irreducible representation πof G such that σ occurs in the restriction of πto 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 [13]. The method may be applied to other classical groups as well.

Original language | English (US) |
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Pages (from-to) | 249-277 |

Number of pages | 29 |

Journal | Journal fur die Reine und Angewandte Mathematik |

Volume | 2020 |

Issue number | 765 |

DOIs | |

State | Published - Aug 1 2020 |

### Bibliographical note

Funding Information:The first named author is partially supported by NSF grant DMS-1600685 and DMS-1901802. The second named author is partially supported by NSF grants DMS-1702218, DMS-1848058, and by start-up funds from the Department of Mathematics at Purdue University. The third named author is partially supported by NSFC grant No.11501382 and by the Fundamental Research Funds for the Central Universities.