Equivalence of domains arising from duality of orbits on flag manifolds III
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. This conjecture was proved for closed S in [WZ2,WZ3,FH,M4] and for open S in [M4]. It was proved for the other orbits in [M5] when GR is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed KC-orbit when GR is of Hermitian type. Thus the conjecture is completely solved affirmatively.
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