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Higgs Bundles, Branes and Langlands Duality

  • Indranil BiswasEmail author
  • Oscar García-Prada
  • Jacques Hurtubise
Article
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Abstract

Given a compact connected Riemann surface X equipped with an anti-holomorphic involution and a complex semisimple Lie group G equipped with a real structure, we define anti-holomorphic involutions on the moduli space of G-Higgs bundles over X. We describe how the various components of the fixed point locus match up, as one passes from G to its Langlands dual LG. As an example, the case of \({G\,=\, {\rm SL}(2,{\mathbb C})}\) and \({^LG\,=\,{\rm PGL}(2,\mathbb{C})}\) is investigated in detail.

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Notes

Acknowledgements

We thank International Centre for Theoretical Sciences for hospitality while a part of the work was carried out. The first author is partially supported by a J. C. Bose Fellowship.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Indranil Biswas
    • 1
    Email author
  • Oscar García-Prada
    • 2
  • Jacques Hurtubise
    • 3
  1. 1.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia
  2. 2.Instituto de Ciencias MatemáticasMadridSpain
  3. 3.Department of MathematicsMcGill UniversityMontrealCanada

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