{
  "id": "1101.1253",
  "version": "v2",
  "published": "2011-01-06T16:59:07.000Z",
  "updated": "2014-07-22T17:34:52.000Z",
  "title": "On Koszul duality for Kac-Moody groups",
  "authors": [
    "Roman Bezrukavnikov",
    "Zhiwei Yun"
  ],
  "comment": "92 pages; with appendices by Zhiwei Yun; final version",
  "journal": "Represent. Theory 17 (2013), 1-98",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "For any Kac-Moody group $G$ with Borel $B$, we give a monoidal equivalence between the derived category of $B$-equivariant mixed complexes on the flag variety $G/B$ and (a certain completion of) the derived category of $B^\\vee$-monodromic mixed complexes on the enhanced flag variety $G^\\vee/U^\\vee$, here $G^\\vee$ is the Langlands dual of $G$. We also prove variants of this equivalence, one of which is the equivalence between the derived category of $U$-equivariant mixed complexes on the partial flag variety $G/P$ and certain \"Whittaker model\" category of mixed complexes on $G^\\vee/B^\\vee$. In all these equivalences, intersection cohomology sheaves correspond to (free-monodromic) tilting sheaves. Our results generalize the Koszul duality patterns for reductive groups in the work of Beilinson, Ginzburg and Soergel .",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-22T17:34:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G44",
      "14M15",
      "14F05"
    ],
    "keywords": [
      "kac-moody group",
      "derived category",
      "equivariant mixed complexes",
      "equivalence",
      "intersection cohomology sheaves correspond"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Represent. Theory"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 92,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1253B"
    }
  }
}