A reciprocal branching problem for automorphic representations and global Vogan packets
A reciprocal branching problem for automorphic representations and global Vogan packets
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DOI：
10.1515/crelle-2019-0016
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发表时间：
2018-12
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影响因子：
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通讯作者：
Dihua Jiang;Baiying Liu;Bin Xu
中科院分区：
文献类型：
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作者：
Dihua Jiang;Baiying Liu;Bin Xu
设G是群，H是G的子群。经典的分支规则（或对称破缺）要求：对于G的一个不可约表示π，确定H的一个不可约表示σ在π到H的限制中的出现。这个经典分支问题的互逆分支问题是：对于H的一个不可约表示σ，找到G的一个不可约表示π，使得σ出现在π到H的限制中。对于经典群的自守表示，分支问题已经由著名的全局Gan-Gross-Prasad猜想解决。本文利用文献[13]中发展的扭自同构下降法研究了特殊正交群的自同构表示的互逆分支问题。该方法也可应用于其他经典群。
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 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 [13]. The method may be applied to other classical groups as well.