Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-01-05825-7
Published electronically: January 18, 2001
MathSciNet review: 1823935
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22E15, 22E10, 32E30, 32M10

Retrieve articles in all journals with MSC (2000): 22E15, 22E10, 32E30, 32M10


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: https://doi.org/10.1090/S0002-9939-01-05825-7
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
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

American Mathematical Society