{
  "id": "0812.1584",
  "version": "v3",
  "published": "2008-12-08T22:48:52.000Z",
  "updated": "2009-05-31T14:24:12.000Z",
  "title": "On the structure of the category O for W-algebras",
  "authors": [
    "Ivan Losev"
  ],
  "comment": "11 pages, v2 some gaps fixed, some proofs rewritten, Remark 5.4 added, v3 15 pages, some gaps fixed, a new section is added",
  "categories": [
    "math.RT"
  ],
  "abstract": "W-algebra (of finite type) W is a certain associative algebra associated with a semisimple Lie algebra, say g, and its nilpotent element, say e. The goal of this paper is to study the category O for W introduced by Brundan, Goodwin and Kleshchev. We establish an equivalence of this category with certain category of g-modules. In the case when e is of principal Levi type (this is always so when g is of type A) the category of g-modules in interest is the category of generalized Whittaker modules introduced McDowel and studied by Milicic-Soergel and Backelin.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-05-31T14:24:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B35"
    ],
    "keywords": [
      "semisimple lie algebra",
      "principal levi type",
      "finite type",
      "generalized whittaker modules",
      "nilpotent element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.1584L"
    }
  }
}