Let
M be a compact connected special flat affine manifold without boundary
equipped with a Gauduchon metric
g and a covariant constant volume form. Let
G be either a connected reductive complex linear algebraic group or the real
locus of a split real form of a complex reductive group. We prove that a flat
principal
G-bundle
over
M admits a Hermitian-Einstein structure if
and only
... [Show full abstract] if is polystable. A polystable flat principal G--bundle over
M admits a unique Hermitian-Einstein connection. We also prove the existence
and uniqueness of a Harder-Narasimhan filtration for flat vector bundles over
M.