## 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.

Publisher Copyright:

© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.