  This article gives matrix factorizations for the trivalent diagrams and
double line appearing in $\mathfrak{sl}_n$ quantum link invariant.
  These matrix factorizations reconstruct Khovanov-Rozansky homology. And we
show that the Euler characteristic of the matrix factorization for a double
loop equals the quantum dimension of the representation $\land^2 V$ of $U_q
(\mathfrak{sl}_n)$ in Section \ref{sec3.3}.
