{
  "id": "1206.0443",
  "version": "v1",
  "published": "2012-06-03T13:36:05.000Z",
  "updated": "2012-06-03T13:36:05.000Z",
  "title": "On Kottwitz' conjecture for twisted involutions",
  "authors": [
    "Meinolf Geck"
  ],
  "comment": "30 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Kottwitz' conjecture is concerned with the intersections of Kazhdan--Lusztig cells with conjugacy classes of involutions in finite Coxeter groups. In joint work with Bonnaf\\'e, we have recently found a way to prove this conjecture for groups of type $B_n$ and $D_n$. The argument for type $D_n$ relies on two ingredients which were used there without proof: (1) a strengthened version of the \"branching rule\" and (2) the consideration of \"$\\diamond$-twisted\" involutions where $\\diamond$ is a graph automorphism. In this paper we deal with (1), (2) and complete the argument for type $D_n$; moreover, we establish Kottwitz' conjecture for $\\diamond$-twisted involutions in all cases where $\\diamond$ is non-trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-03T13:36:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08"
    ],
    "keywords": [
      "twisted involutions",
      "conjecture",
      "finite coxeter groups",
      "joint work",
      "conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0443G"
    }
  }
}