{
  "id": "math/0512046",
  "version": "v1",
  "published": "2005-12-02T04:21:24.000Z",
  "updated": "2005-12-02T04:21:24.000Z",
  "title": "Hermitian representations of the extended affine Lie algebra $\\widetilde{\\frak{gl}_{2}(\\bc_q)}$",
  "authors": [
    "Yun Gao",
    "Ziting Zeng"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We use the idea of free fields to obtain highest weight representations for the extended affine Lie algebra $\\widetilde{\\frak{gl}_{2}(\\bc_q)}$ coordinatized by the quantum torus $\\bc_q$ and go on to construct a contravariant hermitian form. We further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-02T04:21:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G30"
    ],
    "keywords": [
      "extended affine lie algebra",
      "hermitian representations",
      "contravariant hermitian form",
      "highest weight representations",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12046G"
    }
  }
}