{
  "id": "math/0509408",
  "version": "v1",
  "published": "2005-09-19T00:19:49.000Z",
  "updated": "2005-09-19T00:19:49.000Z",
  "title": "Classical symmetric functions in superspace",
  "authors": [
    "Patrick Desrosiers",
    "Luc Lapointe",
    "Pierre Mathieu"
  ],
  "comment": "21 pages, this supersedes the first part of math.CO/0412306",
  "journal": "J Algebr Comb 24 (2006) 209--238",
  "doi": "10.1007/s10801-006-0020-9",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the classical bases, namely, the monomial symmetric functions, the elementary symmetric functions, the completely symmetric functions, and the power sums. Various basic results, such as the generating functions for the multiplicative bases, Cauchy formulas, involution operations as well as the combinatorial scalar product are also generalized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-19T00:19:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical symmetric functions",
      "superspace",
      "symmetric function theory",
      "monomial symmetric functions",
      "elementary symmetric functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9408D"
    }
  }
}