MATRIX FACTORIZATIONS AND INTERTWINERS OF THE FUNDAMENTAL REPRESENTATIONS OF QUANTUM GROUP Uq(sln)

We want to construct a homological link invariant whose Euler characteristic is MOY polynomial as Khovanov and Rozansky constructed a categorification of HOMFLY polynomial. The present paper gives the first step to construct a categorification of MOY polynomial. For the essential colored planar diagrams with additional data which is a sequence naturally induced by coloring, we define matrix factorizations, and then we define a matrix factorization for planar diagram obtained by gluing the essential planar diagrams as tensor product of the matrix factorizations for the essential planar diagrams. Moreover, we show that some matrix factorizations derived from tensor product of the essential matrix factorizations have homotopy equivalences corresponding to MOY relations.