  This is the author's diploma thesis. We describe a simplification in the
construction of Khovanov-Rozansky's categorification of quantum sl(n) link
homology using the theory of maximal Cohen-Macaulay modules over hypersurface
singularities and the combinatorics of Soergel bimodules. More precisely, we
show that the matrix factorizations associated to basic MOY-graphs equal
Cohen-Macaulay approximations of certain Soergel bimodules, and prove that
taking Cohen-Macaulay approximation commutes with tensor products as long as
the MOY-graph under consideration does not possess oriented cycles. It follows
that the matrix factorization associated to a MOY-braid equals the
Cohen-Macaulay approximation of the Soergel bimodule corresponding to the
endofunctor on BGG-category O associated to the braid by Mazorchuk and
Stroppel. This reduces certain computations in the category of matrix
factorizations to known combinatorics of the Hecke-algebra. Finally, we
describe braid closure as some kind of Hochschild cohomology and prove that the
indecomposable Soergel bimodules corresponding to Young tableaux with more than
n rows have trivial Cohen-Macaulay approximation, in analogy to the fact that
the corresponding projective functors on category O vanish on restriction to
parabolics with at most n parts.
