{
  "id": "2011.05564",
  "version": "v1",
  "published": "2020-11-07T03:09:45.000Z",
  "updated": "2020-11-07T03:09:45.000Z",
  "title": "A combinatorial translation principle for the general linear group",
  "authors": [
    "Rudolf Tange"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2011.03606; text overlap with arXiv:0806.4500",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under the assumption that p is bigger than the greatest hook length in the partitions involved. Then we introduce and study the rational Schur functor from a category of GL_n-modules to the category of modules for the walled Brauer algebra. As a corollary we obtain the decomposition numbers for the walled Brauer algebra when $p$ is bigger than the greatest hook length in the partitions involved. This is a sequel to an earlier paper on the symplectic group and the Brauer algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-07T03:09:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear group",
      "combinatorial translation principle",
      "greatest hook length",
      "walled brauer algebra",
      "decomposition numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}