{
  "id": "1709.03004",
  "version": "v1",
  "published": "2017-09-09T20:48:26.000Z",
  "updated": "2017-09-09T20:48:26.000Z",
  "title": "Ringel duality for perverse sheaves on hypertoric varieties",
  "authors": [
    "Tom Braden",
    "Carl Mautner"
  ],
  "comment": "60 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Motivated by the polynomial representation theory of the general linear group and the theory of symplectic singularities, we study a category of perverse sheaves with coefficients in a field $k$ on any affine unimodular hypertoric variety. Our main result is that this is a highest weight category whose Ringel dual is the corresponding category for the Gale dual hypertoric variety. On the way to proving our main result, we confirm a conjecture of Finkelberg-Kubrak in the case of hypertoric varieties. We also show that our category is equivalent to representations of a combinatorially-defined algebra, recently introduced in a related paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-09T20:48:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perverse sheaves",
      "ringel duality",
      "main result",
      "gale dual hypertoric variety",
      "affine unimodular hypertoric variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}