{
  "id": "math/0407522",
  "version": "v1",
  "published": "2004-07-30T04:05:36.000Z",
  "updated": "2004-07-30T04:05:36.000Z",
  "title": "A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$",
  "authors": [
    "Cedric Lecouvey"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Starting from Jacobi-Trudi's type determinental expressions for the Schur functions corresponding to types $B,C$ and $D,$ we define a natural $q$-analogue of the multiplicity $[V(\\lambda):M(\\mu)]$ when $M(\\mu)$ is a tensor product of row or column shaped modules defined by $\\mu$. We prove that these $q$-multiplicities are equal to certain Kostka-Foulkes polynomials related to the root systems $C$ or $D$. Finally we derive formulas expressing the associated multiplicities in terms of Kostka numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-30T04:05:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicity",
      "root systems",
      "tensor product",
      "jacobi-trudis type determinental expressions",
      "schur functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7522L"
    }
  }
}