{
  "id": "1808.08484",
  "version": "v1",
  "published": "2018-08-26T00:00:54.000Z",
  "updated": "2018-08-26T00:00:54.000Z",
  "title": "A super Schur-Weyl reciprocity for cyclotomic Hecke algebras",
  "authors": [
    "Deke Zhao"
  ],
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $U_q(\\mathfrak{g})$ be the quantized superalgebra of $\\mathfrak{g}=\\mathfrak{gl}(k_1|\\ell_1)\\oplus\\cdots\\oplus\\mathfrak{gl}(k_m|\\ell_m)$ and $H_{m,n}(q,\\mathbf{Q})$ the cyclotomic Hecke algebra of type $G(m,1,n)$. We define a right $H_{m,n}(q,\\mathbf{Q})$-action on the $n$-fold tensor (super)space of the vector representation of $U_q(\\mathfrak{g})$ and prove the Schur--Weyl reciprocity between $U_q(\\mathfak{g})$ and $H_{m,n}(q,\\mathbf{Q})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-26T00:00:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclotomic hecke algebra",
      "super schur-weyl reciprocity",
      "fold tensor",
      "vector representation",
      "quantized superalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}