{
  "id": "2307.14608",
  "version": "v1",
  "published": "2023-07-27T03:47:58.000Z",
  "updated": "2023-07-27T03:47:58.000Z",
  "title": "Smooth modules over the N=1 Bondi-Metzner-Sachs superalgebra",
  "authors": [
    "Dong Liu",
    "Yufeng Pei",
    "Limeng Xia",
    "Kaiming Zhao"
  ],
  "comment": "Latex 27pages, comments are welcome!",
  "categories": [
    "math.RT",
    "math.QA",
    "math.RA"
  ],
  "abstract": "In this paper, we present a determinant formula for the contravariant form on Verma modules over the N=1 Bondi-Metzner-Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the N=1 BMS superalgebra. We also utilize the Heisenberg-Clifford vertex superalgebra to construct a free field realization for the N=1 BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the N=1 BMS superalgebra, which includes Fock modules and certain Whittaker modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-27T03:47:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B68",
      "17B69",
      "17B70",
      "81R10"
    ],
    "keywords": [
      "bondi-metzner-sachs superalgebra",
      "free field realization",
      "bms superalgebra",
      "whittaker modules",
      "verma modules"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}