{
  "id": "2107.03173",
  "version": "v1",
  "published": "2021-07-07T12:09:07.000Z",
  "updated": "2021-07-07T12:09:07.000Z",
  "title": "Harish-Chandra bimodules of finite $K$-type in Deligne categories",
  "authors": [
    "Alexandra Utiralova",
    "Serina Hu"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We continue the study of Harish-Chandra bimodules in the setting of the Deligne categories $\\mathrm{Rep}(G_t)$, that was started in the previous work of the first author (arXiv:2002.01555). In this work we construct a family of Harish-Chandra bimodules that generalize simple finite dimensional bimodules in the classical case. It turns out that they have finite $K$-type, which is a non-vacuous condition for the Harish-Chandra bimodules in $\\mathrm{Rep}(G_t)$. The full classification of (simple) finite $K$-type bimodules is yet unknown. This construction also yields some examples of central characters $\\chi$ of the universal enveloping algebra $U(\\mathfrak{g}_t)$ for which the quotient $U_\\chi$ is not simple, and, thereby, it allows us to partially solve a question posed by Pavel Etingof in one of his works.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-07T12:09:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harish-chandra bimodules",
      "deligne categories",
      "generalize simple finite dimensional bimodules",
      "first author",
      "full classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}