{
  "id": "2206.07709",
  "version": "v1",
  "published": "2022-06-15T17:58:41.000Z",
  "updated": "2022-06-15T17:58:41.000Z",
  "title": "On the Grothendieck ring of a quasireductive Lie superalgebra",
  "authors": [
    "Maria Gorelik",
    "Vera Serganova",
    "Alexander Sherman"
  ],
  "comment": "43 pages; comments welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a Lie superalgebra $\\mathfrak{g}$ and a maximal quasitoral subalgebra $\\mathfrak{h}$, we consider properties of restrictions of $\\mathfrak{g}$-modules to $\\mathfrak{h}$. This is a natural generalization of the study of characters in the case when $\\mathfrak{h}$ is an even maximal torus. We study the case of $\\mathfrak{g}=\\mathfrak{q}_n$ with $\\mathfrak{h}$ a Cartan subalgebra, and prove several special properties of the restriction in this case, including an explicit realization of the $\\mathfrak{h}$-supercharacter ring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-15T17:58:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasireductive lie superalgebra",
      "grothendieck ring",
      "maximal quasitoral subalgebra",
      "explicit realization",
      "natural generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}