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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Equivalence of domains arising from duality of orbits on flag manifolds III
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by Toshihiko Matsuki PDF
Trans. Amer. Math. Soc. 359 (2007), 4773-4786 Request permission

Abstract:

In Gindikin and Matsuki 2003, we 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 Wolf and Zierau 2000 and 2003, Fels and Huckleberry 2005, and Matsuki 2006 and for open $S$ in Matsuki 2006. It was proved for the other orbits in Matsuki 2006, when $G_{\mathbb {R}}$ is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed $K_{\mathbb C}$-orbit when $G_{\mathbb {R}}$ 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
  • Received by editor(s): October 20, 2004
  • Received by editor(s) in revised form: April 28, 2005
  • Published electronically: April 24, 2007
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 4773-4786
  • MSC (2000): Primary 14M15, 22E15, 22E46, 32M05
  • DOI: https://doi.org/10.1090/S0002-9947-07-04076-7
  • MathSciNet review: 2320651