{
  "id": "1710.06890",
  "version": "v1",
  "published": "2017-10-18T18:35:55.000Z",
  "updated": "2017-10-18T18:35:55.000Z",
  "title": "Small-dimensional representations of algebraic groups of type $A_l$",
  "authors": [
    "Álvaro L. Martínez"
  ],
  "comment": "13 pages, 3 tables",
  "categories": [
    "math.GR"
  ],
  "abstract": "For $G$ an algebraic group of type $A_l$ over an algebraically closed field of characteristic $p$, we determine all irreducible rational representations of G in defining characteristic with dimensions $\\le (l+1)^s$ for $s = 3, 4$, provided that $l > 18$, $l > 35$ respectively. We also give explicit descriptions of the corresponding modules for $s = 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-18T18:35:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic group",
      "small-dimensional representations",
      "irreducible rational representations",
      "explicit descriptions",
      "algebraically closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}