{
  "id": "1504.01546",
  "version": "v1",
  "published": "2015-04-07T10:56:12.000Z",
  "updated": "2015-04-07T10:56:12.000Z",
  "title": "A general framework for the polynomiality property of the structure coefficients of double-class algebras",
  "authors": [
    "Omar Tout"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Take a sequence of couples $(G_n,K_n)_n$, where $G_n$ is a group and $K_n$ is a sub-group of $G_n.$ Under some conditions, we are able to give a formula that shows the form of the structure coefficients that appear in the product of double-classes of $K_n$ in $G_n.$ We show how this can give us a similar result for the structure coefficients of the centers of group algebras. These formulas allow us to re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair $(\\mathcal{S}_{2n},\\mathcal{B}_{n}).$ We also give a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the double-class algebra $\\mathbb{C}[diag(\\mathcal{S}_{n-1})\\setminus \\mathcal{S}_n\\times \\mathcal{S}^{opp}_{n-1}/ diag(\\mathcal{S}_{n-1})].$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-07T10:56:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15"
    ],
    "keywords": [
      "structure coefficients",
      "polynomiality property",
      "double-class algebra",
      "general framework",
      "symmetric group algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401546T"
    }
  }
}