The moduli space of Hermitian-Yang-Mills connections

In this paper, we study Hermitian-Yang-Mills connections (HYM) on a smooth Hermitian vector bundle over compact K\"{a}hler manifold. We prove that (1) The moduli space of irreducible HYM connections is a complex manifold in a neighbourhood of points satisfying suitable condition. (2) There is an open injection from the moduli space of irreducible HYM connections into the moduli space of simple Higgs structures. We use a similar method as the one used in studying the moduli spaces of Hermitian-Eisntein connections on a smooth Hermitian vector bundle over compact K\"{a}hler manifold.