{
  "id": "1112.2624",
  "version": "v1",
  "published": "2011-12-12T17:07:22.000Z",
  "updated": "2011-12-12T17:07:22.000Z",
  "title": "The Bruhat--Chevalley order on involutions of the hyperoctahedral group and combinatorics of $B$-orbit closures",
  "authors": [
    "Mikhail V. Ignatyev"
  ],
  "comment": "13 pages",
  "journal": "J. Math. Sci. 192 (2013), no. 2, 220-231",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be the symplectic group, $\\Phi=C_n$ its root system, $B\\subset G$ its standard Borel subgroup, $W$ the Weyl group of $\\Phi$. To each involution $\\sigma\\in W$ one can assign the $B$-orbit $\\Omega_{\\sigma}$ contained in the dual space of the Lie algebra of the unipotent radical of $B$. We prove that $\\Omega_{\\sigma}$ is contained in the Zariski closure of $\\Omega_{\\tau}$ if and only of $\\sigma\\leq\\tau$ with respect to the Bruhat--Chevalley order. We also prove that $\\dim\\Omega_{\\sigma}$ is equal to $l(\\sigma)$, the length of $\\sigma$ in $W$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-12T17:07:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B08"
    ],
    "keywords": [
      "bruhat-chevalley order",
      "hyperoctahedral group",
      "orbit closures",
      "involution",
      "combinatorics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.2624I"
    }
  }
}