{
  "id": "1502.06714",
  "version": "v1",
  "published": "2015-02-24T08:52:17.000Z",
  "updated": "2015-02-24T08:52:17.000Z",
  "title": "Monoidal categorification of cluster algebras II",
  "authors": [
    "Seok-Jin Kang",
    "Masaki Kashiwara",
    "Myungho Kim",
    "Se-jin Oh"
  ],
  "comment": "51pages,",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We prove that the quantum unipotent coordinate algebra $A_q(\\mathfrak{n}(w))\\ $ associated with a symmetric Kac-Moody algebra and its Weyl group element $w$ has a monoidal categorification as a quantum cluster algebra. As an application of our earlier work, we achieve it by showing the existence of a quantum monoidal seed of $A_q(\\mathfrak{n}(w))$ which admits the first-step mutations in all the directions. As a consequence, we solve the conjecture that any cluster monomial is a member of the upper global basis up to a power of $q^{1/2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-24T08:52:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "81R50",
      "17B37"
    ],
    "keywords": [
      "monoidal categorification",
      "quantum unipotent coordinate algebra",
      "quantum cluster algebra",
      "upper global basis",
      "weyl group element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}