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Real groups transitive on complex flag manifolds

Author(s): Joseph A. Wolf
Journal: Proc. Amer. Math. Soc. 129 (2001), 2483-2487.
MSC (2000): Primary 22E15; Secondary 22E10, 32E30, 32M10
Posted: January 18, 2001
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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 $G$.

References:

[M]
D. Montgomery, Simply connected homogeneous spaces, Proc. Amer. Math. Soc. 1 (1950), 467-469. MR 12:242c

[O1]
A. L. Onishchik, Inclusion relations among transitive compact transformation groups. Trudy Moskov. Mat. Obsc. 11 (1962), 199-142.
[O2]
A. L. Onishchik, Topology of Transitive Transformation Groups, Johann Ambrosius Barth, Leipzig/Berlin/Heidelberg, 1994. MR 95e:57058

[W1]
J. A. Wolf, The automorphism group of a homogeneous almost complex manifold. Trans. Amer. Math. Soc. 144 (1969), 535-543. MR 41:956

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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
Email: jawolf@math.berkeley.edu

DOI: 10.1090/S0002-9939-01-05825-7
PII: S 0002-9939(01)05825-7
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
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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