A reciprocal branching problem for automorphic representations and global Vogan packets

2018/12/07 by Dihua Jiang, Baiying Liu, Jiang, Dihua +3
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1812.03162

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arxiv created 2018/12/07 · openalex publication_date 2018/12/07 · arxiv updated 2018/12/10 · openalex created_date 2018/12/22 · openalex updated_date 2026/07/28

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 π of G, determine the occurrence of an irreducible representation σ of H in the restriction of π to H. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation σ of H, find an irreducible representation π of G such that σ occurs in the restriction of π 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.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

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