{
  "id": "0712.3117",
  "version": "v1",
  "published": "2007-12-19T08:29:48.000Z",
  "updated": "2007-12-19T08:29:48.000Z",
  "title": "A new approach to Kostant's problem",
  "authors": [
    "Johan Kåhrström",
    "Volodymyr Mazorchuk"
  ],
  "journal": "Algebra and Number Theory 4 (2010), No. 3, 231-254",
  "categories": [
    "math.RT"
  ],
  "abstract": "For every involution $\\mathbf{w}$ of the symmetric group $S_n$ we establish, in terms ofa special canonical quotient of the dominant Verma module associated with $\\mathbf{w}$, an effective criterion, which allows us to verify whether the universal enveloping algebra $U(\\mathfrak{sl}_n)$ surjects onto the space of all ad-finite linear transformations of the simple highest weight module $L(\\mathbf{w})$. An easy sufficient condition derived from this criterion admits a straightforward computational check for example using a computer. All this is applied to get some old and many new results, which answer the classical question of Kostant in special cases, in particular we give a complete answer for simple highest weight modules in the regular block of $\\mathfrak{sl}_n$, $n\\leq 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-19T08:29:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B35"
    ],
    "keywords": [
      "kostants problem",
      "simple highest weight module",
      "terms ofa special canonical quotient",
      "ad-finite linear transformations",
      "symmetric group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3117K"
    }
  }
}