Parabolic Subgroups of Real Direct Limit Lie Groups

Abstract

Let GR be a classical real direct limit Lie group, and gR its Lie algebra. The parabolic subalgebras of the complexification gC were described by the first two authors. In the present paper we extend these results to gR. This also gives a description of the parabolic subgroups of GR. Furthermore, we give a geometric criterion for a parabolic subgroup PC ofGC to intersectGR in a parabolic subgroup. This criterion involves the GR–orbit structure of the flag ind–manifold GC/PC. MSC 2000 : 17B05; 17B65.

Cite this paper

@inproceedings{DanCohen2009ParabolicSO, title={Parabolic Subgroups of Real Direct Limit Lie Groups}, author={Elizabeth Dan-Cohen and Ivan B. Penkov and Joseph Wolf}, year={2009} }