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Higgs bundles, branes and Langlands duality (1707.00392v2)

Published 3 Jul 2017 in math.AG and math.DG

Abstract: Given a compact Riemann surface $X$ and a complex reductive Lie group $G$ equipped with real structures, we define antiholomorphic involutions on the moduli space of $G$-Higgs bundles over $X$. We investigate how the various components of the fixed point locus match up, as one passes from $G$ to its Langlands dual $^LG$. Special attention is given to the case $G=SL(2,\C)$ and $^{LG=PGL(2,\C)$.}