{
  "id": "1509.03269",
  "version": "v1",
  "published": "2015-09-10T18:48:58.000Z",
  "updated": "2015-09-10T18:48:58.000Z",
  "title": "Categorical actions on unipotent representations I. Finite unitary groups",
  "authors": [
    "Olivier Dudas",
    "Michela Varagnolo",
    "Eric Vasserot"
  ],
  "comment": "71 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified representation is naturally isomorphic to a direct sum of level 2 Fock spaces. From our construction we deduce that the Harish-Chandra branching graph coincide with the crystal graph of these Fock spaces, solving a recent conjecture of Gerber-Hiss-Jacon. We also obtain derived equivalences between blocks, yielding Brou\\'e's abelian defect groups conjecture for unipotent $\\ell$-blocks at linear primes $\\ell$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-10T18:48:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite unitary groups",
      "unipotent representations",
      "categorical action",
      "broues abelian defect groups conjecture",
      "fock spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150903269D"
    }
  }
}