{
  "id": "1710.06627",
  "version": "v1",
  "published": "2017-10-18T09:02:31.000Z",
  "updated": "2017-10-18T09:02:31.000Z",
  "title": "Monoidal categories of modules over quantum affine algebras of type A and B",
  "authors": [
    "Masaki Kashiwara",
    "Myungho Kim",
    "Se-jin Oh"
  ],
  "comment": "39pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We construct an exact tensor functor from the category $\\mathcal{A}$ of finite-dimensional graded modules over the quiver Hecke algebra of type $A_\\infty$ to the category $\\mathscr C_{B^{(1)}_n}$ of finite-dimensional integrable modules over the quantum affine algebra of type $B^{(1)}_n$. It factors through the category $\\mathcal T_{2n}$, which is a localization of $\\mathcal{A}$. As a result, this functor induces a ring isomorphism from the Grothendieck ring of $\\mathcal T_{2n}$ (ignoring the gradings) to the Grothendieck ring of a subcategory $\\mathscr C^{0}_{B^{(1)}_n}$ of $\\mathscr C_{B^{(1)}_n}$. Moreover, it induces a bijection between the classes of simple objects. Because the category $\\mathcal T_{2n}$ is related to categories $\\mathscr C^{0}_{A^{(t)}_{2n-1}}$ $(t=1,2)$ of the quantum affine algebras of type $A^{(t)}_{2n-1}$, we obtain an interesting connection between those categories of modules over quantum affine algebras of type $A$ and type $B$. Namely, for each $t =1,2$, there exists an isomorphism between the Grothendieck ring of $\\mathscr C^{0}_{A^{(t)}_{2n-1}}$ and the Grothendieck ring of $\\mathscr C^{0}_{B^{(1)}_n}$, which induces a bijection between the classes of simple modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-18T09:02:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R50",
      "16T25",
      "17B37"
    ],
    "keywords": [
      "quantum affine algebra",
      "monoidal categories",
      "grothendieck ring",
      "quiver hecke algebra",
      "exact tensor functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}