{
  "id": "math/0309314",
  "version": "v3",
  "published": "2003-09-19T06:17:40.000Z",
  "updated": "2004-07-30T02:32:42.000Z",
  "title": "Equivalence of domains arising from duality of orbits on flag manifolds",
  "authors": [
    "Toshihiko Matsuki"
  ],
  "comment": "32 pages; improved many arguments, also updated Remark 1.6",
  "journal": "Trans. Amer. Math. Soc. 358 (2006), 2217--2245.",
  "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 by computing many examples. In this paper, we first prove (in Theorem 1.3 and Corollary 1.4) this conjecture for the open K_C-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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-07-30T02:32:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "22E15",
      "22E46",
      "32M05"
    ],
    "keywords": [
      "flag manifold",
      "domains arising",
      "equivalence",
      "non-hermitian cases",
      "conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9314M"
    }
  }
}