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Homogeneous domains on flag manifolds. (English) Zbl 0632.53047
The paper is concerned with the study of the following problem: for a parabolic subgroup P of a (complex or real) semisimple Lie group L find all subgroups $$G\subset L$$ which act locally transitively on the flag manifold L/P and find all open orbits of these subgroups on L/P. The author solves this problem in the following cases: L is a real simple Lie group of real rank 1; L is a complex simple Lie group, P its maximal parabolic subgroup; L is a real pseudoorthogonal group, L/P the corresponding quadric, G reductive. A characterization of locally transitive subgroups $$G\subset L$$ in terms of representation theory is established. The paper also contains a survey of related results and applications.
Reviewer: A.L.Onishchik

##### MSC:
 53C30 Differential geometry of homogeneous manifolds 22E46 Semisimple Lie groups and their representations
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