{
  "id": "math/0512257",
  "version": "v4",
  "published": "2005-12-13T05:09:31.000Z",
  "updated": "2007-04-10T05:41:27.000Z",
  "title": "Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)",
  "authors": [
    "Takeshi Ikeda",
    "Hiroshi Mizukawa",
    "Tatsuhiro Nakajima",
    "Hiro-Fumi Yamada"
  ],
  "comment": "21pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of \"mixed\" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-04-10T05:41:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "17B67"
    ],
    "keywords": [
      "affine lie algebra",
      "rectangular schur functions",
      "mixed expansion formula",
      "schur s-functions",
      "young diagrams"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12257I"
    }
  }
}