{
  "id": "2103.17093",
  "version": "v1",
  "published": "2021-03-31T14:04:17.000Z",
  "updated": "2021-03-31T14:04:17.000Z",
  "title": "Exceptional collections, t-structures, and categorical action of shifted $q=0$ affine algebra, $\\mathfrak{sl}_{2}$ case",
  "authors": [
    "You-Hung Hsu"
  ],
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "In this article, we show that the categorical action of the shifted $q=0$ affine algebra can be used to construct (or induce) t-structures on the weight categories. The main idea is to interpret the exceptional collection constructed by Kapranov as convolution of Fourier-Mukai kernels in the categorical action via using the Borel-Weil-Bott theorem. In particular, when the categories are the bounded derived category of coherent sheaves on Grassmannians. The t-structure we obtain is precisely the exotic t-structure defined by Bezrukavnikov of the exceptional collections given by Kapranov. As an application, we calculate the matrix coefficients for generators of the shifted $q=0$ affine algebra on the basis given by Kapranov exceptional collections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-31T14:04:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F08",
      "14M15",
      "18G80",
      "16E20",
      "18F30"
    ],
    "keywords": [
      "affine algebra",
      "categorical action",
      "kapranov exceptional collections",
      "main idea",
      "weight categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}