{
  "id": "0712.2695",
  "version": "v3",
  "published": "2007-12-17T11:42:16.000Z",
  "updated": "2008-03-02T02:46:32.000Z",
  "title": "Q-systems as cluster algebras",
  "authors": [
    "Rinat Kedem"
  ],
  "comment": "16 pages, 3 figures",
  "journal": "J.Phys.A41:194011,2008",
  "doi": "10.1088/1751-8113/41/19/194011",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Q-systems first appeared in the analysis of the Bethe equations for the XXX-model and generalized Heisenberg spin chains. Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras, and discuss the relation of the polynomiality property of the solutions of the $Q$-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-03-02T02:46:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster algebras",
      "simple lie algebra",
      "generalized heisenberg spin chains",
      "laurent phenomenon",
      "bethe equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "May",
      "volume": 41,
      "number": 19,
      "pages": 194011
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 775399,
      "adsabs": "2008JPhA...41s4011K"
    }
  }
}