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 | References | Similar Articles | Additional Information

Abstract: S. Gindikin and the author defined a - invariant subset of for each -orbit on every flag manifold and conjectured that the connected component of the identity would be equal to the Akhiezer-Gindikin domain if is of nonholomorphic type. This conjecture was proved for closed in the works of J. A. Wolf, R. Zierau, G. Fels, A. Huckleberry and the author. It was also proved for open by the author. In this paper, we prove the conjecture for all the other orbits when 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

Email:
matsuki@math.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-06-08406-1

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