{
  "id": "2006.03516",
  "version": "v1",
  "published": "2020-06-05T15:43:35.000Z",
  "updated": "2020-06-05T15:43:35.000Z",
  "title": "On the little Weyl group of a real spherical space",
  "authors": [
    "Job J. Kuit",
    "Eitan Sayag"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "In the present paper we further the study of the compression cone of a real spherical homogeneous space $Z=G/H$. In particular we provide a geometric construction of the little Weyl group of $Z$ introduced recently by Knop and Kr\\\"otz. Our technique is based on a fine analysis of limits of conjugates of the subalgebra $\\mathrm{Lie}(H)$ along one-parameter subgroups in the Grassmannian of subspaces of $\\mathrm{Lie}(G)$. The little Weyl group is obtained as a finite reflection group generated by the reflections in the walls of the compression cone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-05T15:43:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "14L30",
      "14M27",
      "20G25",
      "22E46",
      "22F30"
    ],
    "keywords": [
      "little weyl group",
      "real spherical space",
      "compression cone",
      "finite reflection group",
      "geometric construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}