{
  "id": "math/0410302",
  "version": "v1",
  "published": "2004-10-13T01:24:57.000Z",
  "updated": "2004-10-13T01:24:57.000Z",
  "title": "Equivalence of domains arising from duality of orbits on flag manifolds III",
  "authors": [
    "Toshihiko Matsuki"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-13T01:24:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "22E15",
      "22E46",
      "32M05"
    ],
    "keywords": [
      "flag manifold",
      "domains arising",
      "equivalence",
      "conjecture",
      "non-hermitian type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10302M"
    }
  }
}