{
  "id": "1702.08264",
  "version": "v1",
  "published": "2017-02-27T13:08:33.000Z",
  "updated": "2017-02-27T13:08:33.000Z",
  "title": "The dual group of a spherical variety",
  "authors": [
    "Friedrich Knop",
    "Barbara Schalke"
  ],
  "comment": "v1: 30 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $X$ be a spherical variety for a connected reductive group $G$. Work of Gaitsgory-Nadler strongly suggests that the Langlands dual group $G^\\vee$ of $G$ has a subgroup whose Weyl group is the little Weyl group of $X$. Sakellaridis-Venkatesh defined a refined dual group $G^\\vee_X$ and verified in many cases that there exists an isogeny $\\phi$ from $G^\\vee_X$ to $G^\\vee$. In this paper, we establish the existence of $\\phi$ in full generality. Our approach is purely combinatorial and works (despite the title) for arbitrary $G$-varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-27T13:08:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B22",
      "14L30",
      "11F70"
    ],
    "keywords": [
      "spherical variety",
      "little weyl group",
      "langlands dual group",
      "full generality",
      "refined dual group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}