Orbits of real forms in complex flag manifolds

Details Orbits of real forms in complex flag manifolds Orbits of real forms in complex flag manifolds

2006-11-24

arxiv.org/abs/math/0611755v2

Mathematics

Complex Variables

58 pages, AMS-TeX v2 typographical changes

Scientific paper

We study, from the point of view of CR geometry, the orbits M of a real form G of a complex semisimple Lie group G in a complex flag manifold G/Q. In particular we characterize those that are of finite type and satisfy some Levi nondegeneracy conditions. These properties are also graphically described by attaching to them some cross-marked diagrams that generalize those for minimal orbits that we introduced in a previous paper. By constructing canonical fibrations over real flag manifolds, with simply connected complex fibers, we are also able to compute their fundamental group.

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