{
  "id": "2106.08931",
  "version": "v1",
  "published": "2021-06-16T16:41:44.000Z",
  "updated": "2021-06-16T16:41:44.000Z",
  "title": "Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system",
  "authors": [
    "Zengo Tsuboi"
  ],
  "comment": "25 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(2)})$ and the non-twisted quantum affine algebra $U_{q}(so(2r+1)^{(1)})$, we proposed, in the previous paper [arXiv:1109.5524], a Wronskian solution of the T-system for $U_{q}(so(2r+1)^{(1)})$ as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(1)})$. In this paper, we elaborate on this solution, and give a proof missing in [arXiv:1109.5524]. In particular, we explain its connection to the Cherednik-Bazhanov-Reshetikhin (quantum Jacobi-Trudi) type determinant solution known in [arXiv:hep-th/9506167]. We also propose Wronskian-type expressions of T-functions (eigenvalues of transfer matrices) labeled by non-rectangular Young diagrams, which are quantum affine algebra analogues of the Weyl character formula for $so(2r+1)$. We show that T-functions for spinorial representations of $U_{q}(so(2r+1)^{(1)})$ are related to reductions of T-functions for asymptotic typical representations of $U_{q}(gl(2r|1)^{(1)})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-16T16:41:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wronskian solution",
      "boson-fermion correspondence",
      "qq-relations",
      "quantum affine algebra analogues",
      "non-twisted quantum affine algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}