{
  "id": "1212.5375",
  "version": "v3",
  "published": "2012-12-21T10:00:11.000Z",
  "updated": "2014-03-03T16:31:45.000Z",
  "title": "Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$",
  "authors": [
    "Omar Tout"
  ],
  "comment": "32 pages, 15 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Hecke algebra of the pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of $S_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property of its structure coefficients. Our main tool is a combinatorial universal algebra which projects on the Hecke algebra of $(S_{2n},B_n)$ for every $n$. To build it, we introduce new objects called partial bijections.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-03T16:31:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15"
    ],
    "keywords": [
      "hecke algebra",
      "structure coefficients",
      "combinatorial universal algebra",
      "symmetric group algebra",
      "hyperoctahedral subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5375T"
    }
  }
}