2006/04/28 by Ron Donagi, Tony Pantev, Donagi, Ron +1 · 6 citations
Mathematics · Physics and Astronomy · #14A20 #14H40 #14H81 #1H70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT) #hep-th #math.AG #math.RT #msc:14A20 #msc:14H40 #msc:14H81 #msc:1H70
paper · pdf · doi:10.48550/arxiv.math/0604617
75 pages, 1 figure, LaTeX. New version substantially expanded and revised for publication
openalex publication_date 2006/04/28 · arxiv created 2011/12/22 · arxiv updated 2011/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \lanG. In particular, the general fiber of the connected component \Higgs0 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 \lanG. The non-neutral connected components \Higgsα form torsors over \Higgs0. We show that their duals are gerbes over \Higgs0 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 \lanG-Higgs bundles, which incorporates all the previous dualities. All these results extend immediately to an arbirtary connected complex reductive group \mathbbG.