{
  "id": "math/0504041",
  "version": "v1",
  "published": "2005-04-03T09:24:58.000Z",
  "updated": "2005-04-03T09:24:58.000Z",
  "title": "A twisted approach to Kostant's problem",
  "authors": [
    "Volodymyr Mazorchuk"
  ],
  "comment": "16 pages",
  "journal": "Glasg. Math. J. 47 (2005), no. 3, 549-561",
  "categories": [
    "math.RT"
  ],
  "abstract": "We use Arkhipov's twisting functors to show that the universal enveloping algebra of a semi-simple complex finite-dimensional Lie algebra surjects onto the space of ad-finite endomorphisms of the simple highest weight module $L(\\lambda)$, whose highest weight is associated (in the natural way) with a subset of simple roots and a simple root in this subset. This is a new step towards a complete answer to a classical question of Kostant. We also show how one can use the twisting functors to reprove the classical results related to this question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-03T09:24:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B35"
    ],
    "keywords": [
      "kostants problem",
      "twisted approach",
      "semi-simple complex finite-dimensional lie algebra",
      "complex finite-dimensional lie algebra surjects",
      "simple root"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4041M"
    }
  }
}