{
  "id": "math/0309247",
  "version": "v4",
  "published": "2003-09-15T15:47:32.000Z",
  "updated": "2006-06-03T19:23:03.000Z",
  "title": "Perverse sheaves, Koszul IC-modules, and the quiver for the category O",
  "authors": [
    "Maxim Vybornov"
  ],
  "comment": "NEW: final version to appear in Inventiones Mathematicae. Some exposition revisions. Quiver computed explicitly for A_2 in the appendix. 29 pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.RT"
  ],
  "abstract": "For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0. We prove that the category of (mixed) IC-modules is equivalent to the category of (mixed) perverse sheaves for flag varieties. As an application, we describe an algorithm calculating the quiver underlying the BGG category O for arbitrary simple Lie algebra, thus answering a question which goes back to I. M. Gelfand.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-06-03T19:23:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perverse sheaves",
      "koszul ic-modules",
      "arbitrary simple lie algebra",
      "linear algebra devices",
      "flag varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9247V"
    }
  }
}