{
  "id": "1407.7826",
  "version": "v1",
  "published": "2014-07-29T19:08:15.000Z",
  "updated": "2014-07-29T19:08:15.000Z",
  "title": "New Descriptions of Demazure Tableaux and Right Keys, with Applications to Convexity",
  "authors": [
    "Matthew J. Willis"
  ],
  "comment": "Ph. D. thesis completed at University of North Carolina at Chapel Hill in April of 2012",
  "categories": [
    "math.CO"
  ],
  "abstract": "The right key of a semistandard Young tableau is a tool used to find Demazure characters for $sl_n(\\mathbb{C})$. This thesis gives methods to obtain the right and left keys by inspection of the semistandard Young tableau. Given a partition $\\lambda$ and a Weyl group element $w$, there is a semistandard Young tableau $Y_\\lambda(w)$ of shape $\\lambda$ that corresponds to $w$. The Demazure character for $\\lambda$ and $w$ is known to be the sum of the weights of all tableaux whose right key is dominated by $Y_\\lambda(w)$. The set of all such tableaux is denoted $\\mathcal{D}_\\lambda(w)$. Exploiting the method mentioned above for obtaining right keys, this thesis describes the entry at each location in any $T \\in \\mathcal{D}_\\lambda(w)$. Lastly, we will consider $\\mathcal{D}_\\lambda(w)$ as an integral subset of Euclidean space. The final results present a condition that is both necessary and sufficient for this subset to be convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-29T19:08:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "17B10"
    ],
    "keywords": [
      "semistandard young tableau",
      "demazure tableaux",
      "descriptions",
      "applications",
      "demazure character"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7826W"
    }
  }
}