{
  "id": "2107.05024",
  "version": "v1",
  "published": "2021-07-11T11:21:31.000Z",
  "updated": "2021-07-11T11:21:31.000Z",
  "title": "The algebra of conjugacy classes of the wreath product of a finite group with the symmetric group",
  "authors": [
    "Omar Tout"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1902.02124",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\\wr \\mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer coefficients. Our main tool is a combinatorial algebra which projects onto the center of the group $G\\wr \\mathcal{S}_n$ algebra for every $n.$ This generalizes the Ivanov and Kerov method to prove the polynomiality property for the structure coefficients of the center of the symmetric group algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-11T11:21:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wreath product",
      "finite group",
      "conjugacy classes",
      "structure coefficients",
      "symmetric group algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}