Real groups transitive on complex flag manifolds (Q2719026)

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scientific article; zbMATH DE number 1597917
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Real groups transitive on complex flag manifolds
scientific article; zbMATH DE number 1597917

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    Real groups transitive on complex flag manifolds (English)
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    14 May 2001
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    semisimple Lie group
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    semisimple Lie algebra
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    representation
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    flag manifold
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    flag domain
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    The paper under review deals with subgroups \(A\) of a complex connected semisimple Lie group \(G\) acting transitively on a corresponding complex flag manifold \(Z = G/Q\), where \(Q \subseteq G\) is a parabolic subgroup. It contains a complete list of all such subgroups with special attention to those which are real forms of \(G\). Since the compact real forms always act transitively on \(Z\) for trivial reasons, one only has to consider non-compact proper subgroups.
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