{
  "id": "2407.19844",
  "version": "v1",
  "published": "2024-07-29T09:55:48.000Z",
  "updated": "2024-07-29T09:55:48.000Z",
  "title": "Tensor product weight modules over the affine-Virasoro algebra",
  "authors": [
    "Qiu-Fan Chen",
    "Yu-Feng Yao"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique\" established for the Virasoro algebra in [H. Chen, X. Guo, K. Zhao, Tensor product weight modules over the Virasoro algebra, J. Lond. Math. Soc. 88(2013), 829-844.]. All such tensor product modules are indecomposable modules with infinite-dimensional weight spaces. Moreover, we obtain the necessary and sufficient conditions for such tensor product modules to be irreducible. Therefore, we obtain a class of new irreducible weight modules over the affine-Virasoro algebra. Finally, the necessary and sufficient conditions for any two such tensor product modules to be isomorphic are also determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T09:55:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B65",
      "17B67",
      "17B68"
    ],
    "keywords": [
      "tensor product weight modules",
      "affine-virasoro algebra",
      "tensor product modules",
      "sufficient conditions",
      "irreducible highest weight modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}