{
  "id": "math/0001084",
  "version": "v1",
  "published": "2000-01-14T20:03:30.000Z",
  "updated": "2000-01-14T20:03:30.000Z",
  "title": "The Kronecker product of Schur functions indexed by two-row shapes or hook shapes",
  "authors": [
    "Mercedes H. Rosas"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The Kronecker product of two Schur functions $s_{\\mu}$ and $s_{\\nu}$, denoted by $s_{\\mu}*s_{\\nu}$, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions $\\mu$ and $\\nu$. The coefficient of $s_{\\lambda}$ in this product is denoted by $\\gamma^{\\lambda}_{{\\mu}{\\nu}}$, and corresponds to the multiplicity of the irreducible character $\\chi^{\\lambda}$ in $\\chi^{\\mu}\\chi^{\\nu}.$ We use Sergeev's Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for $s_{\\lambda}[XY]$ to find closed formulas for the Kronecker coefficients $\\gamma^{\\lambda}_{{\\mu}{\\nu}}$ when $\\lambda$ is an arbitrary shape and $\\mu$ and $\\nu$ are hook shapes or two-row shapes. Remmel \\cite{Re1, Re2} and Remmel and Whitehead \\cite{Re-Wh} derived some closed formulas for the Kronecker product of Schur functions indexed by two-row shapes or hook shapes using a different approach. We believe that the approach of this paper is more natural. The formulas obtained are simpler and reflect the symmetry of the Kronecker product.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-01-14T20:03:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "05E05"
    ],
    "keywords": [
      "kronecker product",
      "schur functions",
      "hook shapes",
      "two-row shapes",
      "closed formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......1084R"
    }
  }
}