{
  "id": "1905.04630",
  "version": "v1",
  "published": "2019-05-12T02:33:46.000Z",
  "updated": "2019-05-12T02:33:46.000Z",
  "title": "Finite-dimensional representations of hyper multicurrent and multiloop algebras",
  "authors": [
    "Angelo Bianchi",
    "Samuel Chamberlin"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We investigate the categories of finite-dimensional representations of multicurrent and multiloop hyperalgebras in positive characteristic, i.e., the hyperalgebras associated to the multicurrent algebras $\\mathfrak g\\otimes\\mathbb{C}[t_1,\\ldots,t_n]$ and to the multiloop algebras $\\mathfrak g\\otimes\\mathbb{C}[t_1^{\\pm1},\\ldots,t_n^{\\pm 1}]$, where $\\mathfrak g$ is any finite-dimensional complex simple Lie algebra. The main results are the construction of the universal finite-dimensional highest-weight modules and a classification of irreducible modules in each category. In the characteristic zero setting we also provide a relationship between them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-12T02:33:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B10",
      "14L17"
    ],
    "keywords": [
      "finite-dimensional representations",
      "multiloop algebras",
      "hyper multicurrent",
      "finite-dimensional complex simple lie algebra",
      "universal finite-dimensional highest-weight modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}