{
  "id": "2409.16259",
  "version": "v1",
  "published": "2024-09-24T17:29:43.000Z",
  "updated": "2024-09-24T17:29:43.000Z",
  "title": "Perverse sheaves and t-structures on the thin and thick affine flag varieties",
  "authors": [
    "Roman Bezrukavnikov",
    "Calder Morton-Ferguson"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We study the categories $\\mathrm{Perv}_{\\mathrm{thin}}$ and $\\mathrm{Perv}_{\\mathrm{thick}}$ of Iwahori-equivariant perverse sheaves on the thin and thick affine flag varieties associated to a split reductive group $G$. An earlier work of the first author describes $\\mathrm{Perv}_{\\mathrm{thin}}$ in terms of bimodules over the so-called non-commutative Springer resolution. We partly extend this result to $\\mathrm{Perv}_{\\mathrm{thick}}$, providing a similar description for its anti-spherical quotient. The long intertwining functor realizes $\\mathrm{Perv}_{\\mathrm{thick}}$ as the Ringel dual of $\\mathrm{Perv}_{\\mathrm{thin}}$, we point out that it shares some exactness properties with the similar functor acting on perverse sheaves on the finite-dimensional flag variety. We use this result to resolve a conjecture of Arkhipov and the first author, proving that the image in the Iwahori-Whittaker category of any convolution-exact perverse sheaf on the affine flag variety is tilting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-24T17:29:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine flag variety",
      "thick affine flag varieties",
      "first author",
      "t-structures",
      "convolution-exact perverse sheaf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}