{
  "id": "2502.09605",
  "version": "v1",
  "published": "2025-02-13T18:55:38.000Z",
  "updated": "2025-02-13T18:55:38.000Z",
  "title": "Modular reduction of complex representations of finite reductive groups",
  "authors": [
    "Roman Bezrukavnikov",
    "Michael Finkelberg",
    "David Kazhdan",
    "Calder Morton-Ferguson"
  ],
  "comment": "27 pages, 6 figures",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Given a complex representation of a finite group, Brauer and Nesbitt defined in 1941 its reduction mod p, obtaining a representation over the algebraic closure of $\\mathbb{F}_p$. In 2021, Lusztig studied the characters obtained by reducing mod p an irreducible unipotent representation of a finite reductive group over $\\mathbb{F}_p$. He gave a conjectural formula for this character as a linear combination of terms which had no explicit definition and were only known in some small-rank examples. In this paper we provide an explicit formula for these terms and prove Lusztig's conjecture, giving a formula for the reduction mod p of any unipotent representation of $G(\\mathbb{F}_q)$ for q a power of p. We also propose a conjecture linking this construction to the full exceptional collection in the derived category of coherent sheaves on a partial flag variety constructed recently by Samokhin and van der Kallen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-13T18:55:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite reductive group",
      "complex representation",
      "modular reduction",
      "reduction mod",
      "partial flag variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}