{
  "id": "1506.08071",
  "version": "v1",
  "published": "2015-06-26T13:38:34.000Z",
  "updated": "2015-06-26T13:38:34.000Z",
  "title": "Weil representation of a generalized linear group over a ring of truncated polynomials (over a finite field",
  "authors": [
    "Luis Gutiérrez Frez",
    "José Pantoja"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct a complex linear Weil representation $\\rho$ of the generalized special linear group $G=SL_*^{1}(2,A_n)$, ($A_n=K[x]/\\langle x^n\\rangle $, $K$ the quadratic extension of the finite field $k$ of $q$ elements, $q$ odd), where $A_n$ is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of $G$, via linear operators satisfying the relations of the presentation. The structure of a unitary group $U$ associated to $G$ is described. Using this group we obtain a first decomposition of $\\rho$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-26T13:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20C15",
      "20F05"
    ],
    "keywords": [
      "generalized linear group",
      "finite field",
      "truncated polynomials",
      "complex linear weil representation",
      "generalized special linear group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}