{
  "id": "1108.1906",
  "version": "v3",
  "published": "2011-08-09T12:04:21.000Z",
  "updated": "2011-12-29T18:37:41.000Z",
  "title": "Highest weight modules at the critical level and noncommutative Springer resolution",
  "authors": [
    "Roman Bezrukavnikov",
    "Qian Lin"
  ],
  "comment": "13 pages, more typos corrected in this version",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "In arXiv:1001.2562 a certain non-commutative algebra $A$ was defined starting from a semi-simple algebraic group, so that the derived category of $A$-modules is equivalent to the derived category of coherent sheaves on the Springer (or Grothendieck-Springer) resolution. Let $\\hat{\\g}$ be the affine Lie algebra corresponding to the Langlands dual Lie algebra. Using results of Frenkel and Gaitsgory arXiv:0712.0788 we show that the category of $\\hat{\\g}$ modules at the critical level which are Iwahori integrable and have a fixed central character, is equivalent to the category of modules over a quotient of $A$ by a central character. This implies that numerics of Iwahori integrable modules at the critical level is governed by the canonical basis in the $K$-group of a Springer fiber, which was conjecturally described by Lusztig and constructed in arXiv:1001.2562.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-29T18:37:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "highest weight modules",
      "critical level",
      "noncommutative springer resolution",
      "central character",
      "langlands dual lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1906B"
    }
  }
}