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

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

2004-10-13

arxiv.org/abs/math/0410302v1

Mathematics

Representation Theory

15 pages

Scientific paper

In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_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 [WZ2,WZ3,FH,M4] and for open S in [M4]. It was proved for the other orbits in [M5] when G_R is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed K_C-orbit when G_R is of Hermitian type. Thus the conjecture is completely solved affirmatively.

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