{
  "id": "2209.13634",
  "version": "v1",
  "published": "2022-09-27T19:03:44.000Z",
  "updated": "2022-09-27T19:03:44.000Z",
  "title": "Non-archimedean Schur representations of $\\mathrm{GL}(n,R)$ and their invariant lattices",
  "authors": [
    "Yassine EL Maazouz",
    "Antonio Lerario"
  ],
  "comment": "14 pages, 1 Figure",
  "categories": [
    "math.NT",
    "math.AG",
    "math.PR"
  ],
  "abstract": "Let a $K$ be a non-archimedean discretely valued field and $R$ its valuation ring. Given a vector space $V$ of dimension $n$ over $K$ and a partition $\\lambda$ of an integer $d$, we study the problem of determining the invariant lattices in the Schur module $S_\\lambda(V)$ under the action of the group $\\mathrm{GL}(n,R)$. When $K$ is a non-archimedean local field, our results determine the $\\mathrm{GL}(n,R)$-invariant Gaussian distributions on $S_\\lambda(V)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-27T19:03:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G25",
      "12J25",
      "28C10",
      "51E24"
    ],
    "keywords": [
      "non-archimedean schur representations",
      "invariant lattices",
      "non-archimedean local field",
      "invariant gaussian distributions",
      "non-archimedean discretely valued field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}