This paper generalizes the Gan–Gross–Prasad (GGP) conjectures that were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the non-generic L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of Arthur parameters that governs the branching laws for ${{\rm GL}}_n$ and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in Gan et al. [Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I, Astérisque 346 (2012), 1–109] including Bessel models and Fourier–Jacobi models.

中文翻译：

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经典群的分支法则：非回火情况

本文将早先为缓和或更普遍的通用 L 数据包制定的 Gan-Gross-Prasad (GGP) 猜想推广到 Arthur 数据包，特别是对于由 Arthur 参数产生的非通用 L 数据包。该论文介绍了一对相关的 Arthur 参数的关键概念，这些参数控制 ${{\rm GL}}_n$ 的分支定律以及局部域和全局域上的所有经典群。它对 Gan 等人研究的所有分支问题都有作用。经典群表示论中的辛局部根数、中心临界L值和限制问题。Sur les conjectures de Gross et Prasad。I, Astérisque 346 (2012), 1-109] 包括贝塞尔模型和傅立叶-雅各比模型。