The matrix between PBW basis and semicanonical basis of   $U^+(sl_n(\mathbb{C}))$
  In this paper, we prove that the matrix between a special PBW basis and the semicanonical basis of $U^+(sl_n(\mathbb{C}))$ is upper triangular unipotent under any order which is compatible with the partial order $\leq_{deg}$. 
Hongbo Yin, Shunhua Zhang
math.RT math.RA