{
  "id": "2104.08715",
  "version": "v1",
  "published": "2021-04-18T04:50:07.000Z",
  "updated": "2021-04-18T04:50:07.000Z",
  "title": "Non-weight modules over the mirror Heisenberg-Virasoro algebra",
  "authors": [
    "Dongfang Gao",
    "Yao Ma",
    "Kaiming Zhao"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra $\\mathcal{D}$, including Whittaker modules, $\\mathcal{U}(\\mathbb{C} d_0)$-free modules, and their tensor products. More precisely, we give the necessary and sufficient conditions for the Whittaker modules to be irreducible. We determine all $\\mathcal{D}$-module structures on $\\mathcal{U}(\\mathbb{C} d_0)$, and find the necessary and sufficient conditions for these modules to be irreducible. At last we determine the necessary and sufficient conditions for the tensor products of Whittaker modules and $\\mathcal{U}(\\mathbb{C} d_0)$-free modules to be irreducible, and obtain that any two such tensor products are isomorphic if and only if the corresponding Whittaker modules and $\\mathcal{U}(\\mathbb{C} d_0)$-free modules are isomorphic. These lead to many new irreducible non-weight modules over $\\mathcal{D}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-18T04:50:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B65",
      "17B68"
    ],
    "keywords": [
      "mirror heisenberg-virasoro algebra",
      "whittaker modules",
      "sufficient conditions",
      "tensor products",
      "free modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}