{
  "id": "math/0602055",
  "version": "v2",
  "published": "2006-02-03T02:18:02.000Z",
  "updated": "2006-04-03T05:52:42.000Z",
  "title": "A central element in the universal enveloping algebra of type D_n via minor summation formula of Pfaffians",
  "authors": [
    "Takashi Hashimoto"
  ],
  "comment": "version 1.1(corrected typos and added a reference), 17 pages, no figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "It is known that the universal enveloping algebra of the orthogonal Lie algebra of size even has a central element expressed in terms of Pfaffian of a certain matrix alternating along the anti-diagonal (which we call anti-alternating for short) whose entries are in the univerasal enveloping algebra. In this paper, we establish minor summation formulae of Pfaffian for the noncommutative anti-alternating matrix, as well as for commutative anti-alternating matrix. As an application, we show that the eigenvalues on the highest weight modules of the central element given by the Pfaffian can be easily computed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-03T05:52:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B35",
      "15A15"
    ],
    "keywords": [
      "universal enveloping algebra",
      "central element",
      "anti-alternating matrix",
      "highest weight modules",
      "orthogonal lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2055H"
    }
  }
}