{
  "id": "1411.7595",
  "version": "v1",
  "published": "2014-11-27T13:43:55.000Z",
  "updated": "2014-11-27T13:43:55.000Z",
  "title": "From principal series to finite-dimensional solutions of the Yang-Baxter equation",
  "authors": [
    "D. Chicherin",
    "S. E. Derkachov",
    "V. P. Spiridonov"
  ],
  "comment": "33 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group SL(2,C) or Faddeev's modular double. Then we describe its restriction to an irreducible finite-dimensional representation in one or both spaces. In this way we obtain very simple explicit formulas embracing rational and trigonometric finite-dimensional solutions of the Yang-Baxter equation. Finally, we construct these finite-dimensional solutions by means of the fusion procedure and find a nice agreement between two approaches.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-27T13:43:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yang-baxter equation",
      "simple explicit formulas embracing rational",
      "infinite-dimensional principal series representations",
      "trigonometric finite-dimensional solutions",
      "spectral parameter"
    ],
    "publication": {
      "doi": "10.3842/SIGMA.2016.028"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1331465,
      "adsabs": "2014arXiv1411.7595C"
    }
  }
}