典型群表示的限制：例子
Restrictions of representations of classical groups: examples
摘要：
在较早的论文中，我们考虑了局部域和整体域上的典型群的表示论中的几个限制问题。假设不可约表示的Langlands-Vogan参数化，我们为这些约束问题的解制定了精确的表达式。在局部情况下，我们的代数答案给出的朗兰兹参数和某些自然辛根数与他们有关。在全局情况下，用全局$L$ -函数的中心临界值或导数来表示解析解.在本文中，我们验证了一些这些aesturtures在某些低秩的情况下，使用的方法，基地的变化，θ对应，和全球性的论点。
英文摘要：
In an earlier paper, we considered several restriction problems in the representation theory of classical groups over local and global fields. Assuming the Langlands-Vogan parameterization of irreducible representations, we formulated precise conjectures for the solutions of these restriction problems. In the local case, our conjectural answer is given in terms of Langlands parameters and certain natural symplectic root numbers associated to them. In the global case, the conjectural answer is expressed in terms of the central critical value or derivative of a global $L$-function. In this paper we verify several of these conjectures in certain low rank cases, using methods of base change, theta correspondence, and global arguments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
