This paper contains a categorification of the ${\frak sl}(k) $ link invariant using parabolic
singular blocks of category ${\cal {O}} $. Our approach is intended to be as elementary as
possible, providing essentially combinatorial arguments for the main results of Sussan. The
justification that our combinatorial arguments and steps are correct uses non-combinatorial
geometric and representation theoretic results (eg, the Kazhdan-Lusztig and Soergel's
theorems). We take these results as granted and use them like axioms (called {\it Facts\/} in …