Approximate Hermitian-Yang-Mills structures on semistable principal Higgs bundles

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle $ E$ on a compact K"ahler manifold, with structure group a connected linear algebraic reductive group $G$, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure. © 2014, Springer Science+Business Media Dordrecht.