{
  "id": "1110.6881",
  "version": "v1",
  "published": "2011-10-31T18:16:10.000Z",
  "updated": "2011-10-31T18:16:10.000Z",
  "title": "An Explicit Presentation of the Grothendieck Ring of Finitely Generated F_{q}[SL(2,F_{q})]-Modules",
  "authors": [
    "Davide A. Reduzzi"
  ],
  "comment": "11 pages. Comments are welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let p be a prime and q=p^g. We show that the Grothendieck ring of finitely generated F_{q}[SL(2,F_{q})]-modules is naturally isomorphic to the quotient of the polynomial algebra Z[x] by the ideal generated by f^[g](x)-x, where f(x)=sum_{j=0}^{floor(p/2)}(-1)^{j}(p/(p-j))((p-j); j)x^{p-2j}, and the superscript [g] denotes g-fold composition of polynomials. We conjecture that a similar result holds for simply connected semisimple algebraic groups defined and split over a finite field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-31T18:16:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grothendieck ring",
      "explicit presentation",
      "denotes g-fold composition",
      "similar result holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6881R"
    }
  }
}