{
  "id": "math/0301091",
  "version": "v4",
  "published": "2003-01-09T21:16:42.000Z",
  "updated": "2004-10-20T13:49:51.000Z",
  "title": "Matsuki correspondence for the affine Grassmannian",
  "authors": [
    "David Nadler"
  ],
  "comment": "28 pages; final version, to appear in Duke Math J",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We present a version of the Matsuki correspondence for the affine Grassmannian $Gr=G(C((t)))/G(C[[t]])$ of a connected reductive complex algebraic group $G$. The main statement is an anti-isomorphism between the orbit posets of two subgroups of $G(C((t)))$ acting on $Gr$. The first is the polynomial loop group $LG_R$ of a real form $G_R$ of $G$; the second is the loop group $K(C((t)))$ of the complexification $K$ of a maximal compact subgroup $K_c$ of $G_R$. The orbit poset itself turns out to be simple to describe.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2004-10-20T13:49:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine grassmannian",
      "matsuki correspondence",
      "orbit poset",
      "connected reductive complex algebraic group",
      "polynomial loop group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1091N"
    }
  }
}