Simplicity of stable principal sheaves

Abstract

Let M be a compact connected Kahler manifold, and let G be a connected complex reductive linear algebraic group. We prove that a principal G-sheaf on M admits an admissible Einstein-Hermitian connection if and only if the principal G-sheaf is polystable. Using this it is shown that the holomorphic sections of the adjoint vector bundle of a stable principal G-sheaf on M are given by the center of the Lie algebra of G. The Bogomolov inequality is shown to be valid for polystable principal G-sheaves.