{
  "id": "1303.2466",
  "version": "v3",
  "published": "2013-03-11T09:58:02.000Z",
  "updated": "2014-03-09T20:11:17.000Z",
  "title": "Spherical roots of spherical varieties",
  "authors": [
    "Friedrich Knop"
  ],
  "comment": "v1; 19 pages; v2: 19 pages, reformatted to LaTeX, slightly expanded, a couple of minor errors corrected; v3: 19 pages, minor modifications, final version",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this fundamental theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer's classification of spherical rank-1-varieties.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-09T20:11:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M27",
      "14L30",
      "14G17"
    ],
    "keywords": [
      "spherical roots",
      "finite reflection group",
      "little weyl group",
      "fundamental domain",
      "complex spherical variety"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.2466K"
    }
  }
}