Proceedings of the American Mathematical Society

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



Equivalence of domains arising from duality of orbits on flag manifolds II

Author: Toshihiko Matsuki
Journal: Proc. Amer. Math. Soc. 134 (2006), 3423-3428
MSC (2000): Primary 14M15, 22E15, 22E46, 32M05
Published electronically: May 31, 2006
MathSciNet review: 2240651
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Abstract: S. Gindikin and the author defined a $ G_{\mathbb{R}}$- $ K_{\mathbb{C}}$ invariant subset $ C(S)$ of $ G_{\mathbb{C}}$ for each $ K_{\mathbb{C}}$-orbit $ S$ on every flag manifold $ G_{\mathbb{C}}/P$ and conjectured that the connected component $ C(S)_0$ of the identity would be equal to the Akhiezer-Gindikin domain $ D$ if $ S$ is of nonholomorphic type. This conjecture was proved for closed $ S$ in the works of J. A. Wolf, R. Zierau, G. Fels, A. Huckleberry and the author. It was also proved for open $ S$ by the author. In this paper, we prove the conjecture for all the other orbits when $ G_{\mathbb{R}}$ is of non-Hermitian type.

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Additional Information

Toshihiko Matsuki
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

Keywords: Flag manifolds, symmetric spaces, Stein extensions
Received by editor(s): January 20, 2004
Received by editor(s) in revised form: June 29, 2005
Published electronically: May 31, 2006
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2006 American Mathematical Society