{
  "id": "1506.05378",
  "version": "v1",
  "published": "2015-06-17T16:22:01.000Z",
  "updated": "2015-06-17T16:22:01.000Z",
  "title": "Zamolodchikov integrability via rings of invariants",
  "authors": [
    "Pavlo Pylyavskyy"
  ],
  "comment": "21 pages, 16 figures",
  "categories": [
    "math.CO",
    "math.QA",
    "math.RT"
  ],
  "abstract": "Zamolodchikov periodicity is periodicity of certein recursions associated with box products X \\square Y of two finite type Dynkin diagrams. We suggest an affine analog of Zamolodchikov periodicity, which we call Zamolodchikov integrability. We conjecture that it holds for products X \\square Y, where X is a finite type Dynkin diagram and Y is an extended Dynkin diagram. We prove this conjecture for the case of A_m \\square A_{2n-1}^{(1)}. The proof employs cluster structures in certain classical rings of invariants, previously studied by S.~Fomin and the author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-17T16:22:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "05E10",
      "15A72"
    ],
    "keywords": [
      "zamolodchikov integrability",
      "finite type dynkin diagram",
      "invariants",
      "zamolodchikov periodicity",
      "proof employs cluster structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150605378P"
    }
  }
}