Representations of Fundamental Groups of Compact Kahler Manifolds in Solvable Matrix Groups

In the paper we prove a factorization theorem for representations of fundamental groups of compact K\"{a}hler manifolds ({\em K\"{a}hler groups}) into solvable matrix groups. We apply this result to prove that the universal covering of a compact K\"{a}hler manifold with a residually solvable fundamental group is holomorphically convex.