{
  "id": "2311.03156",
  "version": "v1",
  "published": "2023-11-06T14:50:44.000Z",
  "updated": "2023-11-06T14:50:44.000Z",
  "title": "Iwahori-Hecke algebras acting on tensor space by $q$-deformed letter permutations and $q$-partition algebras",
  "authors": [
    "Geetha Thangavelu",
    "Richard Dipper"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $V$ be an $n$-dimensional vector space over some commutative ring $R$. The symmetric group $\\mathfrak S_n$ acts on tensor space $V^{\\otimes r}$ by restricting the natural action of $GL(V)$ on tensor space to its subgroup $\\mathfrak S_n$. We construct an action of the corresponding Iwahori-Hecke algebra $\\mathcal H_{R,q}(\\mathfrak S_n)$ which specializes to the action of $\\mathfrak S_n$, if $q$ is taken to $1$. The centralizing algebra of this action is called $q$-partition algebra $\\mathcal P_{R,q}(n,r)$. We prove, that $\\mathcal P_{R,q}(n,r)$ is isomorphic to the $q$-partition algebra defined by Halverson and Thiem by different means a few years ago.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-06T14:50:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20D15",
      "20C33",
      "20D20"
    ],
    "keywords": [
      "tensor space",
      "partition algebra",
      "deformed letter permutations",
      "iwahori-hecke algebras acting",
      "dimensional vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}