{
  "id": "2401.11367",
  "version": "v1",
  "published": "2024-01-21T01:44:51.000Z",
  "updated": "2024-01-21T01:44:51.000Z",
  "title": "Classifying representations of finite classical groups of Lie type of dimension up to $\\ell^4$",
  "authors": [
    "Luis Gutiérrez Frez",
    "Adrian Zenteno"
  ],
  "comment": "28 pages",
  "categories": [
    "math.RT",
    "math.GR",
    "math.NT"
  ],
  "abstract": "In this article we classify the irreducible representations of finite classical groups $G$ of Lie type of rank $\\ell$ with dimension at most a constant proportional to $\\ell^4$ according to whether $G$ is of type $A_{\\ell}$ or not. The dimensions of those representations are explicitly computed by hand. We conclude the work by addressing certain cases of the inverse Galois problem via the foregoing classification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-21T01:44:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20G40",
      "11F80"
    ],
    "keywords": [
      "finite classical groups",
      "lie type",
      "classifying representations",
      "inverse galois problem",
      "constant proportional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}