Harmonic Bundles with Symplectic Structures

Abstract

We study harmonic bundles with an additional structure called symplectic structure. We study them for the case of the base manifold is compact and non-compact. For the compact case, we show that a harmonic bundle with a symplectic structure is equivalent to principle $Sp(2n,C)$-bundle with a reductive flat connection. For the non-compact case, we show that a polystable good filtered Higgs bundle with a perfect skew-symmetric pairing is equivalent to a good wild harmonic bundle with a symplectic structure.