{
  "id": "1606.06939",
  "version": "v1",
  "published": "2016-06-22T13:18:53.000Z",
  "updated": "2016-06-22T13:18:53.000Z",
  "title": "On bases of some simple modules of symmetric groups and Hecke algebras",
  "authors": [
    "Melanie de Boeck",
    "Anton Evseev",
    "Sinead Lyle",
    "Liron Speyer"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider simple modules for a Hecke algebra with a parameter of quantum characteristic $e$. Equivalently, we consider simple modules $D^{\\lambda}$, labelled by $e$-restricted partitions $\\lambda$ of $n$, for a cyclotomic KLR algebra $R_n^{\\Lambda_0}$ over a field of characteristic $p\\ge 0$, with mild restrictions on $p$. If all parts of $\\lambda$ are at most $2$, we identify a set $\\mathsf{DStd}_{e,p}(\\lambda)$ of standard $\\lambda$-tableaux, which is defined combinatorially and naturally labels a basis of $D^{\\lambda}$. In particular, we prove that the $q$-character of $D^{\\lambda}$ can be described in terms of $\\mathsf{DStd}_{e,p}(\\lambda)$. We show that a certain natural approach to constructing a basis of an arbitrary $D^{\\lambda}$ does not work in general, giving a counterexample to a conjecture of Mathas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-22T13:18:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C08",
      "05E10"
    ],
    "keywords": [
      "simple modules",
      "hecke algebra",
      "symmetric groups",
      "cyclotomic klr algebra",
      "natural approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}