Matrix factorizations and double line in $\mathfrak{sl}

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126471This 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}.17 pagesGeometric TopologyQuantum Algebra18G60Matrix factorizations and double line in $\mathfrak{sl}_n$ quantum link invarianttext