{
  "id": "2310.12566",
  "version": "v1",
  "published": "2023-10-19T08:19:18.000Z",
  "updated": "2023-10-19T08:19:18.000Z",
  "title": "On representations of the Lie superalgebra p(n)",
  "authors": [
    "Vera Serganova"
  ],
  "comment": "Article from 2002. 15 pages",
  "journal": "Journal of Algebra, Volume 258, Issue 2, 15 December 2002, Pages 615-630",
  "doi": "10.1016/S0021-8693(02)00645-2",
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce a new way to study representations of the Lie superalgebra $p(n)$. Since the center of the universal enveloping algebra $U$ acts trivially on all irreducible representations, we suggest to study the quotient algebra $\\bar{U}$ by the radical of $U$. We show that $\\bar{U}$ has a large center which separates typical finite dimensional irreducible representations. We give a description of $\\bar{U}$ factored by a generic central character. Using this description we obtain character formulae of generic (infinite-dimensional) irreducible representations. We also describe some geometric properties of the supervariety $Spec Gr \\bar{U}$ in the coadjoint representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-19T08:19:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie superalgebra",
      "typical finite dimensional irreducible representations",
      "generic central character",
      "separates typical finite dimensional irreducible",
      "large center"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}