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Rosso-Yamane Theorem on PBW basis of $U_q(A_N)$

arXiv:0804.0954

Abstract

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 $U_q(A_N)$.