{
  "id": "0812.1078",
  "version": "v3",
  "published": "2008-12-05T05:45:15.000Z",
  "updated": "2009-03-08T14:10:35.000Z",
  "title": "Open Orbits and Augmentations of Dynkin Diagrams",
  "authors": [
    "Sin Tsun Edward Fan",
    "Naichung Conan Leung"
  ],
  "comment": "After the first version was posted, we were informed that many of the results in it were obtained earlier by Kac, Rubenthaler and Vinberg. See Remark 1 for more details",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "Given any representation V of a complex linear reductive Lie group G_0, we show that a larger semi-simple Lie group G with g=g_0 + V + V* + ..., exists precisely when V has a finite number of G_0-orbits. In particular, V admits an open G_0-orbit. Furthermore, this corresponds to an augmentation of the Dynkin diagram of g_0. The representation theory of g should be useful in describing the geometry of manifolds with stable forms as studied by Hitchin.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-03-08T14:10:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "17B10"
    ],
    "keywords": [
      "dynkin diagram",
      "open orbits",
      "augmentation",
      "complex linear reductive lie group",
      "larger semi-simple lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.1078F"
    }
  }
}