{
  "id": "1202.0987",
  "version": "v3",
  "published": "2012-02-05T18:19:39.000Z",
  "updated": "2015-09-17T14:11:12.000Z",
  "title": "The $ξ$-stability on the affine grassmannian",
  "authors": [
    "Zongbin Chen"
  ],
  "comment": "23 pages, Published version on Mathematische Zeitschrift",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We introduce a notion of $\\xi$-stability on the affine grassmannian $\\xx$ for the classical groups, this is the local version of the $\\xi$-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient $\\xx^{\\xi}/T$ of the stable part $\\xx^{\\xi}$ by the maximal torus $T$ exists as an ind-$k$-scheme, and we introduce a reduction process analogous to the Harder-Narasimhan reduction for vector bundles. For the group $\\mathrm{SL}_{d}$, we calculate the Poincar\\'e series of the quotient $\\xx^{\\xi}/T$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-06T14:07:19.000Z",
      "comment": "22 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-09-17T14:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E67"
    ],
    "keywords": [
      "affine grassmannian",
      "poincare series",
      "vector bundles",
      "local version",
      "harder-narasimhan reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0987C"
    }
  }
}