The matrix between PBW basis and semicanonical basis of $U^{+}(s{l}_n(\mathbb{C}))$

In this paper, we prove that the matrix between a special PBW basis and the semicanonical basis of $U^{+}(s{l}_n(\mathbb{C}))$ is upper triangular unipotent under any order which is compatible with the partial order ${\le }_{deg}$.