{
  "id": "2005.04838",
  "version": "v1",
  "published": "2020-05-11T02:27:32.000Z",
  "updated": "2020-05-11T02:27:32.000Z",
  "title": "PBW theoretic approach to the module category of quantum affine algebras",
  "authors": [
    "Masaki Kashiwara",
    "Myungho Kim",
    "Se-jin Park",
    "Euiyong Park"
  ],
  "comment": "9 pages. This is an announcement paper whose details will appear elsewhere",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $U_q'(\\mathfrak{g})$ be a quantum affine algebra of untwisted affine ADE type and let $\\mathcal{C}^0_{\\mathfrak{g}}$ be Hernandez-Leclerc's category. For a duality datum $\\mathcal{D}$ in $\\mathcal{C}^0_{\\mathfrak{g}}$, we denote by $\\mathcal{F}_{\\mathcal{D}}$ the quantum affine Weyl-Schur duality functor. We give sufficient conditions for a duality datum $\\mathcal{D}$ to provide the functor $\\mathcal{F}_{\\mathcal{D}}$ sending simple modules to simple modules. Then we introduce the notion of cuspidal modules in $\\mathcal{C}^0_{\\mathfrak{g}}$, and show that all simple modules in $\\mathcal{C}^0_{\\mathfrak{g}}$ can be constructed as the heads of ordered tensor products of cuspidal modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-11T02:27:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "81R50",
      "18D10"
    ],
    "keywords": [
      "quantum affine algebra",
      "pbw theoretic approach",
      "module category",
      "simple modules",
      "quantum affine weyl-schur duality functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}