{
  "id": "1907.07868",
  "version": "v1",
  "published": "2019-07-18T04:26:40.000Z",
  "updated": "2019-07-18T04:26:40.000Z",
  "title": "A note on $q$-oscillator realizations of $U_{q}(gl(M|N))$ for Baxter $Q$-operators",
  "authors": [
    "Zengo Tsuboi"
  ],
  "comment": "33 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra $U_{q}(gl(M|N))$, and obtain q-oscillator realizations of the contracted algebras proposed in [arXiv:1205.1471]. Instead of factoring out the invariant subspaces, we make reduction on generators of the q-oscillator algebra, which gives a shortcut to the problem. Based on this result, we obtain explicit q-oscillator representations of a Borel subalgebra of the quantum affine superalgebra $U_{q}(\\hat{gl}(M|N))$ for Baxter Q-operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-18T04:26:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit q-oscillator representations",
      "quantum affine superalgebra",
      "quantum superalgebra",
      "q-oscillator realizations",
      "asymptotic limits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}