{
  "id": "1311.3170",
  "version": "v1",
  "published": "2013-11-13T15:27:55.000Z",
  "updated": "2013-11-13T15:27:55.000Z",
  "title": "The Dynkin index and sl(2)-subalgebras of simple Lie algebras",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "This is a continuation of arXiv:0903.0398 [math.RT]. Let g be a simple Lie algebra. In this note, we provide simple formulae for the index of sl(2)-subalgebras in the classical Lie algebras and a new formula for the index of the principal sl(2). We also compute the difference, D, of the indices of principal and subregular sl(2)-subalgebras. Our formula for D involves some data related to the McKay correspondence for g. Using the index of sl(2)-subalgebras of classical Lie algebras, we also obtain three series of interesting combinatorial identities parameterised by partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-13T15:27:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B20",
      "17B10",
      "17B22"
    ],
    "keywords": [
      "simple lie algebra",
      "dynkin index",
      "classical lie algebras",
      "subregular sl",
      "simple formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3170P"
    }
  }
}