{
  "id": "1004.1669",
  "version": "v1",
  "published": "2010-04-10T01:38:29.000Z",
  "updated": "2010-04-10T01:38:29.000Z",
  "title": "Quantizations of nilpotent orbits vs 1-dimensional representations of W-algebras",
  "authors": [
    "Ivan Losev"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let g be a semisimple Lie algebra over an algebraically closed field K of characteristic 0 and O be a nilpotent orbit in g. Then Orb is a symplectic algebraic variety and one can ask whether it is possible to quantize $\\Orb$ (in an appropriate sense) and, if so, how to classify the quantizations. On the other hand, for the pair (g,O) one can construct an associative algebra W called a (finite) W-algebra. The goal of this paper is to clarify a relationship between quantizations of O (and of its coverings) and 1-dimensional W-modules. In the first approximation, our result is that there is a one-to-one correspondence between the two. The result is not new: it was discovered (in a different form) by Moeglin in the 80's.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-10T01:38:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B35",
      "53D55"
    ],
    "keywords": [
      "nilpotent orbit",
      "quantizations",
      "representations",
      "semisimple lie algebra",
      "symplectic algebraic variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1669L"
    }
  }
}