{
  "id": "1802.04864",
  "version": "v1",
  "published": "2018-02-13T21:31:15.000Z",
  "updated": "2018-02-13T21:31:15.000Z",
  "title": "Surveying the quantum group symmetries of integrable open spin chains",
  "authors": [
    "Rafael I. Nepomechie",
    "Ana L. Retore"
  ],
  "comment": "48 pages",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "Using anisotropic R-matrices associated with affine Lie algebras $\\hat g$ (specifically, $A_{2n}^{(2)}, A_{2n-1}^{(2)}, B_n^{(1)}, C_n^{(1)}, D_n^{(1)}$) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of $\\hat g$. We show that these transfer matrices also have a duality symmetry (for the cases $C_n^{(1)}$ and $D_n^{(1)}$) and additional $Z_2$ symmetries that map complex representations to their conjugates (for the cases $A_{2n-1}^{(2)}, B_n^{(1)}, D_n^{(1)}$). A key simplification is achieved by working in a certain \"unitary\" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-13T21:31:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable open spin chains",
      "quantum group symmetries",
      "transfer matrices",
      "integrable open quantum spin chains",
      "unbroken symmetry generators appear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}