{
  "id": "1912.03325",
  "version": "v1",
  "published": "2019-12-06T19:35:35.000Z",
  "updated": "2019-12-06T19:35:35.000Z",
  "title": "Coherent categorification of quantum loop algebras : the $SL(2)$ case",
  "authors": [
    "Peng Shan",
    "Michela Varagnolo",
    "Eric Vasserot"
  ],
  "comment": "58 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct an equivalence of graded Abelian categories from a category of representations of the quiver-Hecke algebra of type $A_1^{(1)}$ to the category of equivariant perverse coherent sheaves on the nilpotent cone of type $A$. We prove that this equivalence is weakly monoidal. This gives a representation-theoretic categorification of the preprojective K-theoretic Hall algebra considered by Schiffmann-Vasserot. Using this categorification, we compare the monoidal categorification of the quantum open unipotent cells of type $A_1^{(1)}$ given by Kang-Kashiwara-Kim-Oh-Park in terms of quiver-Hecke algebras with the one given by Cautis-Williams in terms of equivariant perverse coherent sheaves on the affine Grassmannians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-06T19:35:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum loop algebras",
      "coherent categorification",
      "equivariant perverse coherent sheaves",
      "quiver-hecke algebra",
      "quantum open unipotent cells"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}