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

Author:
Toshihiko Matsuki

Journal:
Trans. Amer. Math. Soc. **359** (2007), 4773-4786

MSC (2000):
Primary 14M15, 22E15, 22E46, 32M05

Published electronically:
April 24, 2007

MathSciNet review:
2320651

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Abstract | References | Similar Articles | Additional Information

Abstract: In Gindikin and Matsuki 2003, we 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 Wolf and Zierau 2000 and 2003, Fels and Huckleberry 2005, and Matsuki 2006 and for open in Matsuki 2006. It was proved for the other orbits in Matsuki 2006, when is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed -orbit when is of Hermitian type. Thus the conjecture is completely solved affirmatively.

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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:
http://dx.doi.org/10.1090/S0002-9947-07-04076-7

Keywords:
Flag manifolds,
symmetric spaces,
Stein extensions

Received by editor(s):
October 20, 2004

Received by editor(s) in revised form:
April 28, 2005

Published electronically:
April 24, 2007

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.