{
  "id": "1901.07020",
  "version": "v1",
  "published": "2019-01-21T18:14:20.000Z",
  "updated": "2019-01-21T18:14:20.000Z",
  "title": "Tensor products and $q$-characters of HL-modules and monoidal categorifications",
  "authors": [
    "Matheus Brito",
    "Vyjayanthi Chari"
  ],
  "comment": "36 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite--dimensional representations of a quantum affine algebra of type $A$. We classify the set of prime representations in these subcategories and give necessary and sufficient conditions for a tensor product of two prime representations to be irreducible. In the case of a reducible tensor product we describe the prime decomposition of the simple factors. As a consequence we prove that these subcategories are monoidal categorifications of a cluster algebra of type $A$ with coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-21T18:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "20G42",
      "13F60"
    ],
    "keywords": [
      "tensor product",
      "monoidal categorifications",
      "hl-modules",
      "prime representations",
      "characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}