{
  "id": "math/0502082",
  "version": "v1",
  "published": "2005-02-04T04:47:44.000Z",
  "updated": "2005-02-04T04:47:44.000Z",
  "title": "Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables",
  "authors": [
    "Nantel Bergeron",
    "Christophe Reutenauer",
    "Mercedes Rosas",
    "Mike Zabrocki"
  ],
  "comment": "30 pages",
  "journal": "Canad. J. Math. 60 (2008), no. 2, 266-296",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there exist a natural inclusion of the Hopf algebra of noncommutative symmetric functions indexed by compositions in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-04T04:47:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05A18"
    ],
    "keywords": [
      "symmetric group",
      "noncommuting variables",
      "coinvariants",
      "noncommutative symmetric functions",
      "natural hopf algebra structure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2082B"
    }
  }
}