{
  "id": "1908.08502",
  "version": "v1",
  "published": "2019-08-22T17:17:17.000Z",
  "updated": "2019-08-22T17:17:17.000Z",
  "title": "A Pieri rule for Demazure characters of the general linear group",
  "authors": [
    "Sami Assaf",
    "Danjoseph Quijada"
  ],
  "comment": "65 pages, 28 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Pieri rule is a nonnegative, multiplicity-free formula for the Schur function expansion of the product of an arbitrary Schur function with a single row Schur function. Key polynomials are characters of Demazure modules for the general linear group that generalize the Schur function basis of symmetric functions to a basis of the full polynomial ring. We prove a nonsymmetric generalization of the Pieri rule by giving a cancellation-free, multiplicity-free formula for the key polynomial expansion of the product of an arbitrary key polynomial with a single part key polynomial. Our proof is combinatorial, generalizing the Robinson--Schensted--Knuth insertion algorithm on tableaux to an insertion algorithm on Kohnert diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T17:17:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear group",
      "pieri rule",
      "demazure characters",
      "polynomial",
      "multiplicity-free formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}