{
  "id": "1506.06570",
  "version": "v1",
  "published": "2015-06-22T12:39:24.000Z",
  "updated": "2015-06-22T12:39:24.000Z",
  "title": "Modular representations and branching rules for affine and cyclotomic Yokonuma-Hecke algebras",
  "authors": [
    "Weideng Cui",
    "Jinkui Wan"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We establish an equivalence between a module category of the affine (resp. cyclotomic) Yokonuma-Hecke algebra $\\widehat{Y}_{r,n}(q)$ (resp. $Y_{r,n}^{\\lambda}(q)$) and its suitable counterpart for a direct sum of tensor products of affine Hecke algebras of type $A$ (resp. cyclotomic Hecke algebras). We then develop several applications of this result. The simple modules of affine Yokonuma-Hecke algebras and of their associated cyclotomic Yokonuma-Hecke algebras are classified over an algebraically closed field of characteristic $p=0$ or $(p,r)=1.$ The modular branching rules for these algebras are obtained, and they are further identified with crystal graphs of integrable modules for quantum affine algebras of type $A.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-22T12:39:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching rules",
      "modular representations",
      "associated cyclotomic yokonuma-hecke algebras",
      "affine yokonuma-hecke algebras",
      "affine hecke algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150606570C"
    }
  }
}