{
  "id": "1907.09353",
  "version": "v1",
  "published": "2019-07-22T14:51:08.000Z",
  "updated": "2019-07-22T14:51:08.000Z",
  "title": "Minimal Parabolic $k$-subgroups acting on Symmetric $k$-varieties Corresponding to $k$-split Groups",
  "authors": [
    "Mark Hunnell"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Symmetric $k$-varieties are a natural generalization of symmetric spaces to general fields $k$. We study the action of minimal parabolic $k$-subgroups on symmetric $k$-varieties and define a map that embeds these orbits within the orbits corresponding to algebraically closed fields. We develop a condition for the surjectivity of this map in the case of $k$-split groups that depends only on the dimension of a maximal $k$-split torus contained within the fixed point group of the involution defining the symmetric $k$-variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-22T14:51:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal parabolic",
      "split groups",
      "subgroups acting",
      "varieties corresponding",
      "general fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}