AI 中文总结
本文研究实约化李群Weyl群到半单对称空间$G/H$的推广，证明其Weyl群结构与子代数、对合选择无关，可通过关联李群Weyl群理解其元素，为推广到球形齐性空间奠定基础。
AI 中文摘要
本文研究将实约化李群的Weyl群概念推广到半单对称空间$G/H$。首先证明$G/H$的Weyl群的群结构与$G/H$的分裂Cartan子代数的选择、以及稳定$H$的$G$的Cartan对合的选择无关；之后可通过比较与$G/H$相关的某个约化李群的Weyl群来理解$G/H$的Weyl群的所有元素。为将这些结果推广到实约化球形齐性空间，本工作是该方向的第一步。
英文摘要
This paper investigates a generalization of the notion of the Weyl group of a real reductive Lie group to a semisimple symmetric space $G/H$. First, we show that the group structure of the Weyl group of $G/H$ is independent of the choice of split Cartan subalgebras of $G/H$ and the choice of Cartan involutions of $G$ stabilizing $H$. After that, we can understand all elements of the Weyl group of $G/H$ by comparing the Weyl group of some reductive Lie group associated to $G/H$. With the aim of extending these results to reductive real spherical homogeneous spaces, this work serves as a first step in this direction.
Comments17 pages
