{
  "id": "1608.02447",
  "version": "v1",
  "published": "2016-08-08T14:23:18.000Z",
  "updated": "2016-08-08T14:23:18.000Z",
  "title": "Shifted symmetric functions and multirectangular coordinates of Young diagrams",
  "authors": [
    "Per Alexandersson",
    "Valentin Féray"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "In this paper, we study shifted Schur functions $S_\\mu^\\star$, as well as a new family of shifted symmetric functions $\\mathfrak{K}_\\mu$ linked to Kostka numbers. We prove that both are polynomials in multi-rectangular coordinates, with nonnegative coefficients when written in terms of falling factorials. We then propose a conjectural generalization to the Jack setting. This conjecture is a lifting of Knop and Sahi's positivity result for usual Jack polynomials and resembles recent conjectures of Lassalle. We prove our conjecture for one-part partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-08T14:23:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "20C30"
    ],
    "keywords": [
      "shifted symmetric functions",
      "multirectangular coordinates",
      "young diagrams",
      "study shifted schur functions",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}