Finiteness of orbit structure for real flag manifolds

✍ Scribed by Joseph A. Wolf

• Publisher: Springer
• Year: 1974
• Tongue: English
• Weight: 377 KB
• Volume: 3
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181328

✦ Synopsis

Let G be a reductive real Lie group, a an involutive automorphism of (7, and L = G u the fixed point set of a. 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 a-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.