{
  "id": "0711.4670",
  "version": "v3",
  "published": "2007-11-29T08:47:57.000Z",
  "updated": "2008-11-25T12:43:27.000Z",
  "title": "Automorphism groups of root systems matroids",
  "authors": [
    "Mathieu Dutour Sikiric",
    "Anna Felikson",
    "Pavel Tumarkin"
  ],
  "comment": "9 pages, 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a root system $\\mathsf{R}$, the vector system $\\tilde{\\mathsf{R}}$ is obtained by taking a representative $v$ in each antipodal pair $\\{v, -v\\}$. The matroid $M(\\mathsf{R})$ is formed by all independent subsets of $\\tilde{\\mathsf{R}}$. The automorphism group of a matroid is the group of permutations preserving its independent subsets. We prove that the automorphism groups of all irreducible root systems matroids $M(\\mathsf{R})$ are uniquely determined by their independent sets of size 3. As a corollary, we compute these groups explicitly, and thus complete the classification of the automorphism groups of root systems matroids.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-11-25T12:43:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "independent subsets",
      "irreducible root systems matroids",
      "vector system",
      "antipodal pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4670D"
    }
  }
}