{
  "id": "2001.03760",
  "version": "v1",
  "published": "2020-01-11T14:32:49.000Z",
  "updated": "2020-01-11T14:32:49.000Z",
  "title": "Representations of automorphism groups on the homology of matroids",
  "authors": [
    "Luca Moci",
    "Gian Marco Pezzoli"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT",
    "math.AT",
    "math.CO"
  ],
  "abstract": "Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats of $M$, and (when $M$ is realizable) with the top cohomology of a hyperplane arrangement. Finally we analyze in detail the case of the complete graph, which has applications to algebraic geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-11T14:32:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism groups",
      "representations",
      "dual matroid",
      "algebraic geometry",
      "hyperplane arrangement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}