{
  "id": "1803.10918",
  "version": "v2",
  "published": "2018-03-29T03:39:49.000Z",
  "updated": "2021-01-19T15:37:56.000Z",
  "title": "A simplified presentation of Specht modules",
  "authors": [
    "Sarah Brauner",
    "Tamar Friedmann"
  ],
  "comment": "Fixed mistake in Theorem 2.5. Section 3 has been rewritten to better reflect motivation, and all technical details have been moved to an appendix. Previous appendix has been removed",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We simplify a dual straightening algorithm which gives a presentation of Specht modules as a quotient of the space of column tabloids by dual Garnir relations. We show that this presentation can be generated by a single relation for each pair of columns of a tableau with ordered columns, thereby significantly reducing the number of generators given in the original construction. Our presentation applies to all Specht modules, and is of a similar nature to a recent result by Friedmann-Hanlon-Stanley-Wachs that applies to staircase partitions. We then discuss applications of our simplified presentation to a generalization of the multilinear component of the free Lie algebra studied by Friedmann, Hanlon, Stanley and Wachs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-01-19T15:37:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C30"
    ],
    "keywords": [
      "specht modules",
      "simplified presentation",
      "free lie algebra",
      "dual garnir relations",
      "original construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}