{
  "id": "2102.00979",
  "version": "v1",
  "published": "2021-02-01T17:02:23.000Z",
  "updated": "2021-02-01T17:02:23.000Z",
  "title": "Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$",
  "authors": [
    "Qiu-Fan Chen",
    "Yu-Feng Yao"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of irreducibles defined in [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro algebra of type $A_1$, J. Math. Phys. 60, 071707 (2019)] with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type $A_1$, and give sufficient and necessary conditions for these induced modules to be reducible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T17:02:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B65",
      "17B68",
      "17B70"
    ],
    "keywords": [
      "irreducible tensor product modules",
      "affine-virasoro algebra",
      "non-weight modules",
      "irreducible highest weight modules",
      "induced modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}