{
  "id": "1512.04627",
  "version": "v1",
  "published": "2015-12-15T02:29:48.000Z",
  "updated": "2015-12-15T02:29:48.000Z",
  "title": "Positivity of affine charge",
  "authors": [
    "Avinash J. Dalal"
  ],
  "comment": "17 pages, 3 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "The branching of (k-1)-Schur functions into k-Schur functions was given by Lapointe, Lam, Morse and Shimozono as chains in a poset on k-shapes. The k-Schur functions are the parameterless case of a more general family of symmetric functions over Q(t), conjectured to satisfy a k-branching formula given by weights on the k-shape poset. A concept of a (co)charge on a k-tableau was defined by Lapointe and Pinto. Although it is not manifestly positive, they prove it is compatible with the k-shape poset for standard k-tableau and the positivity follows. Morse introduced a manifestly positive notion of affine (co)charge on k-tableaux and conjectured that it matches the statistic of Lapointe-Pinto. Here we prove her conjecture and the positivity of k-(co)charge for semi-standard tableaux follows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-15T02:29:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "affine charge",
      "positivity",
      "k-shape poset",
      "k-schur functions",
      "symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204627D"
    }
  }
}