{
  "id": "0809.0663",
  "version": "v2",
  "published": "2008-09-03T16:22:57.000Z",
  "updated": "2008-09-15T08:36:38.000Z",
  "title": "Commutative quotients of finite W-algebras",
  "authors": [
    "Alexander Premet"
  ],
  "comment": "35 pages; one subsection added, some typos corrcted",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let U(g,e) be the finite W-algebra associated with a nilpotent element e in a simple Lie algebra g and assume that e is induced from a nilpotent element e_0 in a Levi subalgebra l of g. We show that if the finite W-algebra U(l,e_0) has a 1-dimensional representation, then so does U(g,e). For g classical (and in may other cases), we compute the Krull dimension of the largest commutative quotient of U(g,e). Some applications to representation theory of modular counterparts of g are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-15T08:36:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B45",
      "17B35"
    ],
    "keywords": [
      "finite w-algebra",
      "nilpotent element",
      "simple lie algebra",
      "representation theory",
      "levi subalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0663P"
    }
  }
}