{
  "id": "1708.03038",
  "version": "v1",
  "published": "2017-08-10T00:38:22.000Z",
  "updated": "2017-08-10T00:38:22.000Z",
  "title": "Generalized Springer correspondence for symmetric spaces associated to orthogonal groups",
  "authors": [
    "Toshiaki Shoji",
    "Gao Yang"
  ],
  "comment": "76 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G = GL_N$ over an algebraically closed field of odd characteristic, and $\\theta$ an involutive automorphism on $G$ such that $H = (G^{\\theta})^0$ is isomorphic to $SO_N$. Then $G^{\\iota\\theta} = \\{ g \\in G \\mid \\theta(g) = g^{-1} \\}$ is regarded as a symmetric space $G/G^{\\theta}$. Let $G^{\\iota\\theta}_{uni}$ be the set of unipotent elements in $G^{\\iota\\theta}$. $H$ acts on $G^{\\iota\\theta}_{uni}$ by the conjugation. As an analogue of the generalized Springer correspondence in the case of reductive groups, we establish in this paper the generalized Springer correspondence between $H$-orbits in $G^{\\iota\\theta}_{uni}$ and irreducible representations of various symmetric groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-10T00:38:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G40"
    ],
    "keywords": [
      "generalized springer correspondence",
      "symmetric space",
      "orthogonal groups",
      "unipotent elements",
      "symmetric groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 76,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}