{
  "id": "2303.08267",
  "version": "v1",
  "published": "2023-03-14T22:54:48.000Z",
  "updated": "2023-03-14T22:54:48.000Z",
  "title": "Koszul duality for Coxeter groups",
  "authors": [
    "Simon Riche",
    "Cristian Vay"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct a \"Koszul duality\" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beilinson-Ginzburg-Soergel and Bezrukavnikov-Yun in a geometric context, and of the first author with Achar, Makisumi and Williamson. As an application, we show that the combinatorics of the \"tilting perverse sheaves\" considered in arXiv:1802.07651 is encoded in the combinatorics of the canonical basis of the Hecke algebra of $(W,S)$ attached to the dual realization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-14T22:54:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "koszul duality",
      "coxeter groups",
      "hecke category",
      "coxeter system",
      "dual realization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}