{
  "id": "1710.05326",
  "version": "v1",
  "published": "2017-10-15T12:50:43.000Z",
  "updated": "2017-10-15T12:50:43.000Z",
  "title": "On the action of the Steenrod-Milnor operations on the invariants of the general linear groups",
  "authors": [
    "Nguyen Thai Hoa",
    "Pham Thi Kim Minh",
    "Nguyen Sum"
  ],
  "comment": "7 pages",
  "journal": "Quynhon University Journal of Science, Vol. 7, No. 3 (2013), 5-12",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $p$ be an odd prime number. Denote by $GL_n = GL(n,\\mathbb F_p)$ the general linear group over the prime field $\\mathbb F_p$. Each subgroup of $GL_n$ acts on the algebra $P_n=E(x_1,\\ldots,x_n)\\otimes \\mathbb F_p(y_1,\\ldots,y_n)$ in the usual manner. We grade $P_n$ by assigning $\\dim x_i=1$ and $\\dim y_i=2.$ This algebra is a module over the mod $p$ Steenrod algebra $\\mathcal A_p$. The purpose of the paper is to compute the action of the Steenrod-Milnor operations on the generators of $P_2^{GL_2}$. More precisely, we explicitly determine the action of $St^{(i,j)}$ on the Dickson invariants $Q_{2,0}$ and $Q_{2,1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-15T12:50:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S10",
      "55S05"
    ],
    "keywords": [
      "general linear group",
      "steenrod-milnor operations",
      "odd prime number",
      "usual manner",
      "steenrod algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}