Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$
  Let $U_q(A_N)$ be the Drinfeld-Jimbo quantum group of type $A_N$. In this paper, by using Groebner-Shirshov bases, we give a simple (but not short) proof of the Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$. 
Yuqun Chen, Hongshan Shao and K. P. Shum