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Real groups transitive on complex flag manifolds

Author: Joseph A. Wolf
Journal: Proc. Amer. Math. Soc. 129 (2001), 2483-2487
MSC (2000): Primary 22E15; Secondary 22E10, 32E30, 32M10
Published electronically: January 18, 2001
MathSciNet review: 1823935
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Abstract: Let $Z = G/Q$ be a complex flag manifold. The compact real form $G_u$ of $G$ is transitive on $Z$. If $G_0$ is a noncompact real form, such transitivity is rare but occasionally happens. Here we work out a complete list of Lie subgroups of $G$ transitive on $Z$ and pick out the cases that are noncompact real forms of $G$.

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Additional Information

Joseph A. Wolf
Affiliation: Institut für Mathematik, Ruhr–Universität Bochum, D-44780 Bochum, Germany; Department of Mathematics, University of California, Berkeley, California 94720–3840

Keywords: Semisimple Lie group, semisimple Lie algebra, representation, flag manifold, flag domain
Received by editor(s): July 28, 1999
Received by editor(s) in revised form: December 9, 1999
Published electronically: January 18, 2001
Additional Notes: The author’s research was supported by the Alexander von Humboldt Foundation and by NSF Grant DMS 97-05709. The author thanks the Ruhr–Universität Bochum for hospitality.
Communicated by: Rebecca A. Herb
Article copyright: © Copyright 2001 American Mathematical Society

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