{
  "id": "2408.05103",
  "version": "v1",
  "published": "2024-08-09T14:46:51.000Z",
  "updated": "2024-08-09T14:46:51.000Z",
  "title": "Koszul duality for generalized steinberg representations of $p$-adic groups",
  "authors": [
    "Clifton Cunningham",
    "James Steele"
  ],
  "comment": "22 pages, no figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we prove a novel result on two categories that appear in the local Langlands correspondence, for generalized Steinberg representations. Let $G$ be a semisimple reductive group split over a $p$-adic field $F$. The main result of this paper shows that category of modules over the extension algebra of generalized Steinberg representations of $G(F)$ appears as a full subcategory of equivariant perverse sheaves on the variety of Langlands parameters for these representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-09T14:46:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "22E50",
      "35A27",
      "32S30"
    ],
    "keywords": [
      "generalized steinberg representations",
      "koszul duality",
      "adic groups",
      "local langlands correspondence",
      "equivariant perverse sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}