{
  "id": "2405.06158",
  "version": "v1",
  "published": "2024-05-10T00:41:24.000Z",
  "updated": "2024-05-10T00:41:24.000Z",
  "title": "An example of the Jantzen filtration of a D-module",
  "authors": [
    "Simon Bohun",
    "Anna Romanov"
  ],
  "comment": "24 pages, 8 figures",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We compute the Jantzen filtration of a D-module on the flag variety of $\\mathrm{SL}_2(\\mathbb{C})$. At each step in the computation, we illustrate the $\\mathfrak{sl}_2(\\mathbb{C})$-module structure on global sections to give an algebraic picture of this geometric computation. We conclude by showing that the Jantzen filtration on the D-module agrees with the algebraic Jantzen filtration on its global sections, demonstrating a famous theorem of Beilinson--Bernstein.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-10T00:41:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global sections",
      "algebraic jantzen filtration",
      "geometric computation",
      "algebraic picture",
      "module structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}