Finiteness of orbit structure for real flag manifolds
Finiteness of orbit structure for real flag manifolds
复制标题
实旗流形轨道结构的有限性
DOI：
10.1007/bf00181328
复制
发表时间：
1974
影响因子：
0.5
通讯作者：
J. Wolf
中科院分区：
文献类型：
--
作者：
J. Wolf
设G是一个约化真实的李群，σ是G的一个对合自同构，L=Gσ是σ的不动点集.证明了G只有2/3个抛物子群的L-共轭类，所以如果P是G的抛物子群，则在真实的旗流形G/P上只有2/3个L-轨道.这是通过证明G只有2/3个σ-稳定Cartan子群的L-共轭类来实现的.这些结果推广了G是复群且L是G的真实的形式的已知事实。
Let G be a reductive real Lie group, σ an involutive automorphism of G, and L=Gσ the fixed point set of σ. It is shown that G has only finitely many L-conjugacy classes of parabolic subgroups, so if P is a parabolic subgroup of G then there are only finitely many L-orbits on the real flag manifold G/P. This is done by showing that G has only finitely many L-conjugacy classes of σ-stable Cartan subgroups. These results extend known facts for the case where G is a complex group and L is a real form of G.