{
  "id": "math/0506555",
  "version": "v3",
  "published": "2005-06-27T21:38:34.000Z",
  "updated": "2007-02-20T11:07:25.000Z",
  "title": "Crystal bases and simple modules for Hecke algebras of type G(p,p,n)",
  "authors": [
    "Jun Hu"
  ],
  "comment": "38 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We apply the crystal basis theory for Fock spaces over quantum affine algebras to the modular representations of the cyclotomic Hecke algebras of type $G(p,p,n)$. This yields a classification of simple modules over these cyclotomic Hecke algebras in the non-separated case, generalizing our previous work [J. Hu, J. Algebra 267 (2003) 7-20]. The separated case was completed in [J. Hu, J. Algebra 274 (2004) 446--490]. Furthermore, we use Naito--Sagaki's work [S. Naito & D. Sagaki, J. Algebra 251 (2002) 461--474] on Lakshmibai--Seshadri paths fixed by diagram automorphisms to derive explicit formulas for the number of simple modules over these Hecke algebras. These formulas generalize earlier results of [M. Geck, Represent. Theory 4 (2000) 370-397] on the Hecke algebras of type $D_n$ (i.e., of type $G(2,2,n)$).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-02-20T11:07:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "20C20"
    ],
    "keywords": [
      "simple modules",
      "crystal bases",
      "cyclotomic hecke algebras",
      "crystal basis theory",
      "formulas generalize earlier results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6555H"
    }
  }
}