{
  "id": "1212.6789",
  "version": "v3",
  "published": "2012-12-30T22:48:46.000Z",
  "updated": "2017-07-07T19:51:27.000Z",
  "title": "Semistandard Tableaux for Demazure Characters (Key Polynomials) and Their Atoms",
  "authors": [
    "Robert A. Proctor",
    "Matthew J. Willis"
  ],
  "comment": "19 pages w/ 3 figures (1 new), 1 page with post-publication minor improvements. New title. This is the final pre-typesetting version of the European Journal of Combinatorics paper 43 (2015), 172-184. This v3 has many revisions and clarifications that were inspired by the referees' reports. These include Proposition 1.1, plus the added hypothesis for Theorem 3.2 and for Corollaries 10.2 and 10.6",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Schur function indexed by a partition lambda with at most n parts is the sum of the weight monomials for the Young tableaux of shape lambda. Let pi be an n-permutation. We give two descriptions of the tableaux that contribute their monomials to the key polynomial indexed by pi and lambda. (These polynomials are the characters of the Demazure modules for GL(n).) The \"atom\" indexed by pi is the sum of weight monomials of the tableaux whose right keys are the \"key\" tableau for pi. Schur functions and key polynomials can be decomposed into sums of atoms. We also describe the tableaux that contribute to an atom, the tableaux that have a left key equal to a given key, and the tableaux that have a left key bounded below by a given key.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-26T18:09:43.000Z",
      "title": "Tableaux for Key Polynomials, Demazure Characters, and Atoms",
      "comment": "16 pages, 2 figures. Two paragraphs on potential applications added to introduction, two references for earlier descriptions added, a few sentences added in various places, a couple dozen small wording (or notation) improvements or typo fixes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-07-07T19:51:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "17B10"
    ],
    "keywords": [
      "demazure characters",
      "polynomial",
      "weight monomials",
      "schur function",
      "demazure modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.6789P"
    }
  }
}