{
  "id": "1910.08302",
  "version": "v1",
  "published": "2019-10-18T08:08:18.000Z",
  "updated": "2019-10-18T08:08:18.000Z",
  "title": "The intrinsic hyperplane arrangement in an arbitrary irreducible representation of the symmetric group",
  "authors": [
    "N. Tsilevich",
    "A. Vershik",
    "S. Yuzvinsky"
  ],
  "comment": "18 pp. Ref 11",
  "categories": [
    "math.CO"
  ],
  "abstract": "For every irreducible complex representation~$\\pi_\\lambda$ of the symmetric group~$\\S_n$, we construct, in a canonical way, a so-called intrinsic hyperplane arrangement~$\\A_{\\lambda}$ in the space of~$\\pi_\\lambda$. This arrangement is a direct generalization of the classical braid arrangement (which is the special case of our construction corresponding to the natural representation of~$\\S_n$), has a natural description in terms of invariant subspaces of Young subgroups, and enjoys a number of remarkable properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-18T08:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10"
    ],
    "keywords": [
      "intrinsic hyperplane arrangement",
      "arbitrary irreducible representation",
      "symmetric group",
      "young subgroups",
      "classical braid arrangement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}