{
  "id": "0910.3024",
  "version": "v1",
  "published": "2009-10-16T02:59:36.000Z",
  "updated": "2009-10-16T02:59:36.000Z",
  "title": "Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables",
  "authors": [
    "Francois Bergeron",
    "Aaron Lauve"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We analyze the structure of the algebra N of symmetric polynomials in non-commuting variables in so far as it relates to its commutative counterpart. Using the \"place-action\" of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of N analogous to the classical theorems of Chevalley, Shephard-Todd on finite reflection groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-16T02:59:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "16W30"
    ],
    "keywords": [
      "symmetric polynomials",
      "non-commuting variables",
      "coinvariant spaces",
      "finite reflection groups",
      "tensor product decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.3024B"
    }
  }
}