Equivalence of domains arising from duality of orbits on flag manifolds
Toshihiko Matsuki
Abstract
In [GM1], we defined a GR-KC invariant subset C(S) of GC for each KC-orbit S on every flag manifold GC/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 by computing many examples. In this paper, we first prove (in Theorem 1.3 and Corollary 1.4) this conjecture for the open KC-orbit S on an ``arbitrary'' flag manifold generalizing the result of Barchini. This conjecture for closed S was solved in [WZ1], [WZ2] (Hermitian cases) and [FH] (non-Hermitian cases). We also deduce an alternative proof of this result for non-Hermitian cases from Theorem 1.3.
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