{
  "id": "math/0602660",
  "version": "v2",
  "published": "2006-02-28T11:28:22.000Z",
  "updated": "2007-06-08T10:11:03.000Z",
  "title": "Symmetric products, linear representations and the commuting scheme",
  "authors": [
    "Francesco Vaccarino"
  ],
  "comment": "Accepted for publication on \"Journal of Algebra\", Elsevier. 9 pages",
  "categories": [
    "math.AG",
    "math.AC",
    "math.RT"
  ],
  "abstract": "We show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices. As a consequence we give a surjection from the ring of invariants of several matrices to the ring of multisymmetric functions generalizing a classical result of H.Weyl and F.Junker. We also find a surjection from the ring of invariants over the commuting scheme to the ring of multisymmetric functions. This surjection is an isomophism over a characteristic zero field and induces an isomorphism at the level of reduced structures over an infinite field of positive characteristic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-08T10:11:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "13A50",
      "14A15"
    ],
    "keywords": [
      "commuting scheme",
      "linear representations",
      "symmetric products",
      "multisymmetric functions",
      "characteristic zero field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2660V"
    }
  }
}