{
  "id": "2206.04900",
  "version": "v1",
  "published": "2022-06-10T06:51:56.000Z",
  "updated": "2022-06-10T06:51:56.000Z",
  "title": "On the Unicity and the Ambiguity of Lusztig Parametrizations for Finite Classical Groups",
  "authors": [
    "Shu-Yen Pan"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "The Lusztig correspondence is a bijective mapping between the Lusztig series indexed by the conjugacy class of a semisimple element $s$ in the connected component $(G^*)^0$ of the dual group of $G$ and the set of irreducible unipotent characters of the centralizer of $s$ in $G^*$. In this article we discuss the unicity and ambiguity of such a bijective correspondence. In particular, we show that the Lusztig correspondence for a classical group can be made to be unique if we require it to be compatible with the parabolic induction and the finite theta correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-10T06:51:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33"
    ],
    "keywords": [
      "finite classical groups",
      "lusztig parametrizations",
      "lusztig correspondence",
      "finite theta correspondence",
      "conjugacy class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}