{
  "id": "1904.13040",
  "version": "v1",
  "published": "2019-04-30T03:47:14.000Z",
  "updated": "2019-04-30T03:47:14.000Z",
  "title": "Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young's seminormal basis",
  "authors": [
    "Ming Fang",
    "Kay Jin Lim",
    "Kai Meng Tan"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p>0$, $\\Delta(\\lambda)$ denote the Weyl module of $G$ of highest weight $\\lambda$ and $\\iota_{\\lambda,\\mu}:\\Delta(\\lambda+\\mu)\\to \\Delta(\\lambda)\\otimes\\Delta(\\mu)$ be the canonical $G$-morphism. We study the split condition for $\\iota_{\\lambda,\\mu}$ over $\\mathbb{Z}_{(p)}$, and apply this as an approach to compare the Jantzen filtrations of the Weyl modules $\\Delta(\\lambda)$ and $\\Delta(\\lambda+\\mu)$. In the case when $G$ is of type $A$, we show that the split condition is closely related to the product of certain Young symmetrizers and is further characterized by the denominator of a certain Young's seminormal basis vector in certain cases. We obtain explicit formulas for the split condition in some cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-30T03:47:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20C30"
    ],
    "keywords": [
      "weyl module",
      "young symmetrizers",
      "jantzen filtration",
      "split condition",
      "denominator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}