{
  "id": "2008.07847",
  "version": "v1",
  "published": "2020-08-18T10:51:23.000Z",
  "updated": "2020-08-18T10:51:23.000Z",
  "title": "Representations of quantum affine algebras in their $R$-matrix realization",
  "authors": [
    "Naihuan Jing",
    "Ming Liu",
    "Alexander Molev"
  ],
  "comment": "29 pages; includes a review of arXiv:1705.08155, arXiv:1903.00204 and arXiv:1911.03496",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B,C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix realization. We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the $R$-matrix and Drinfeld presentations of the Yangians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-18T10:51:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum affine algebras",
      "matrix realization",
      "drinfeld presentations",
      "isomorphisms",
      "gauss decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}