{
  "id": "0903.5003",
  "version": "v1",
  "published": "2009-03-28T21:19:52.000Z",
  "updated": "2009-03-28T21:19:52.000Z",
  "title": "Young tableaux and the Steenrod algebra",
  "authors": [
    "Grant Walker",
    "R M W Wood"
  ],
  "comment": "This is the version published by Geometry & Topology Monographs on 14 November 2007",
  "journal": "Geom. Topol. Monogr. 11 (2007) 379-397",
  "doi": "10.2140/gtm.2007.11.379",
  "categories": [
    "math.AT"
  ],
  "abstract": "The purpose of this paper is to forge a direct link between the hit problem for the action of the Steenrod algebra A on the polynomial algebra P(n)=F_2[x_1,...,x_n], over the field F_2 of two elements, and semistandard Young tableaux as they apply to the modular representation theory of the general linear group GL(n,F_2). The cohits Q^d(n)=P^d(n)/P^d(n)\\cap A^+(P(n)) form a modular representation of GL(n,F_2) and the hit problem is to analyze this module. In certain generic degrees d we show how the semistandard Young tableaux can be used to index a set of monomials which span Q^d(n). The hook formula, which calculates the number of semistandard Young tableaux, then gives an upper bound for the dimension of Q^d(n). In the particular degree d where the Steinberg module appears for the first time in P(n) the upper bound is exact and Q^d(n) can then be identified with the Steinberg module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-28T21:19:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S10",
      "20C20"
    ],
    "keywords": [
      "steenrod algebra",
      "semistandard young tableaux",
      "upper bound",
      "hit problem",
      "general linear group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5003W"
    }
  }
}