{
  "id": "hep-th/9405138",
  "version": "v2",
  "published": "1994-05-21T16:43:58.000Z",
  "updated": "1994-05-22T16:23:37.000Z",
  "title": "Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters",
  "authors": [
    "Anthony J. Bracken",
    "Gustav W. Delius",
    "Mark D. Gould",
    "Yao-Zhong Zhang"
  ],
  "comment": "13 pages",
  "journal": "J.Phys. A27 (1994) 6551-6562",
  "doi": "10.1088/0305-4470/27/19/025",
  "categories": [
    "hep-th",
    "math.QA"
  ],
  "abstract": "We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1994-05-22T16:23:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum yang-baxter equation",
      "extra non-additive parameters",
      "spectral parameter",
      "admit non-trivial one-parameter families",
      "quantum non-compact algebras"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 38068
    }
  }
}