{
  "id": "math/0604617",
  "version": "v3",
  "published": "2006-04-28T05:00:40.000Z",
  "updated": "2011-12-22T01:16:02.000Z",
  "title": "Langlands duality for Hitchin systems",
  "authors": [
    "Ron Donagi",
    "Tony Pantev"
  ],
  "comment": "75 pages, 1 figure, LaTeX. New version substantially expanded and revised for publication",
  "categories": [
    "math.AG",
    "hep-th",
    "math.RT"
  ],
  "abstract": "We show that the Hitchin integrable system for a simple complex Lie group $G$ is dual to the Hitchin system for the Langlands dual group $\\lan{G}$. In particular, the general fiber of the connected component $\\Higgs_0$ of the Hitchin system for $G$ is an abelian variety which is dual to the corresponding fiber of the connected component of the Hitchin system for $\\lan{G}$. The non-neutral connected components $\\Higgs_{\\alpha}$ form torsors over $\\Higgs_0$. We show that their duals are gerbes over $\\Higgs_0$ which are induced by the gerbe of $G$-Higgs bundles $\\gHiggs$. More generally, we establish a duality between the gerbe $\\gHiggs$ of $G$-Higgs bundles and the gerbe $\\lan{\\gHiggs}$ of $\\lan{G}$-Higgs bundles, which incorporates all the previous dualities. All these results extend immediately to an arbirtary connected complex reductive group $\\mathbb{G}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-22T01:16:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A20",
      "14H40",
      "14H81"
    ],
    "keywords": [
      "hitchin system",
      "langlands duality",
      "higgs bundles",
      "connected component",
      "simple complex lie group"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 75,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 715845,
      "adsabs": "2006math......4617D"
    }
  }
}