紧致连通李群的极大环面子群

Maximal Torus Subgroup of Connected Compact Lie groups

极大环面子群在李群结构及其表示理论中都是十分重要的。每个连通紧李群具有极大环面子群,任二极大环面子群彼此共轭,且连通紧李群中每个元素共轭于极大环面的一个元素。用对称空间的有关知识给出了极大子环群定理的详细证明。

The maximal torus is essential to the structure and the representation of the compact Lie groups. Every connected, compact Lie groups G contains a maximal torus T. This maximal torus is unique up to conjugation, and every element of G is conjugate to the element of the maximal torus. In this thesis we offer detailed proof of main theorem on tori which take symmetric space as the main tool.