{
  "id": "1112.6189",
  "version": "v2",
  "published": "2011-12-28T22:11:02.000Z",
  "updated": "2014-09-03T06:59:18.000Z",
  "title": "Vertex operators and 2-representations of quantum affine algebras",
  "authors": [
    "Sabin Cautis",
    "Anthony Licata"
  ],
  "comment": "50 pages. Strengthened main result and simplified exposition",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We construct 2-representations of quantum affine algebras from 2-representations of quantum Heisenberg algebras. The main tool in this construction are categorical vertex operators, which are certain complexes in a Heisenberg 2-representation that recover vertex operators after passing to the Grothendieck group. As an application we categorify the Frenkel-Kac-Segal homogeneous realization of the basic representation of (simply laced) quantum affine algebras. This gives rise to categorical actions of quantum affine (and toroidal) algebras on derived categories of coherent sheaves on Hilbert schemes of points of ALE spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-28T22:11:02.000Z",
      "comment": "60 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-03T06:59:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R50",
      "18D05",
      "14F05"
    ],
    "keywords": [
      "quantum affine algebras",
      "quantum heisenberg algebras",
      "main tool",
      "categorical vertex operators",
      "grothendieck group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1083465,
      "adsabs": "2011arXiv1112.6189C"
    }
  }
}