{
  "id": "1607.02803",
  "version": "v1",
  "published": "2016-07-11T01:42:10.000Z",
  "updated": "2016-07-11T01:42:10.000Z",
  "title": "Parallelotope tilings and $q$-decomposition numbers",
  "authors": [
    "Joseph Chuang",
    "Hyohe Miyachi",
    "Kai Meng Tan"
  ],
  "comment": "72 pages, 11 figures",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of $U_q(\\widehat{\\mathfrak{sl}}_e)$. These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the $\\mathrm{Ext}^1$-quivers of $v$-Schur algebras at complex $e$-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the $1$-skeletons of the polytopal complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-11T01:42:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "20G43"
    ],
    "keywords": [
      "decomposition numbers",
      "parallelotope tilings",
      "canonical basis vectors",
      "fock space representation",
      "form polytopal complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 72,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}