Equivalence of domains arising from duality of orbits on flag manifolds II
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- by Toshihiko Matsuki
- Proc. Amer. Math. Soc. 134 (2006), 3423-3428
- DOI: https://doi.org/10.1090/S0002-9939-06-08406-1
- Published electronically: May 31, 2006
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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.References
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Bibliographic Information
- Toshihiko Matsuki
- Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
- Email: matsuki@math.kyoto-u.ac.jp
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 3423-3428
- MSC (2000): Primary 14M15, 22E15, 22E46, 32M05
- DOI: https://doi.org/10.1090/S0002-9939-06-08406-1
- MathSciNet review: 2240651