{
  "id": "math/0610510",
  "version": "v1",
  "published": "2006-10-17T08:54:55.000Z",
  "updated": "2006-10-17T08:54:55.000Z",
  "title": "Pfaffians and Representations of the Symmetric Group",
  "authors": [
    "Alain Lascoux"
  ],
  "comment": "28 p",
  "categories": [
    "math.CO"
  ],
  "abstract": "Pfaffians of matrices with entries z[i,j]/(x\\_i+x\\_j), or determinants of matrices with entries z[i,j]/(x\\_i-x\\_j), where the antisymmetrical indeterminates z[i,j] satisfy the Pl\\\"ucker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young's orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-17T08:54:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric group",
      "youngs orthogonal bases",
      "write explicit expressions",
      "determinants",
      "antisymmetrical indeterminates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10510L"
    }
  }
}