Abstract
Let $U^+$ be the plus part of the quantized enveloping algebra of a simple Lie algebra of type $A_n$ and let $\mathcal{B}^*$ be the dual canonical basis of $U^+$ . Let $b$, $b'$ be in $\mathcal{B}^*$ , and suppose that one of the two elements is a $q$ -commuting product of quantum flag minors. It is shown that $b$ and $b'$ are multiplicative if and only if they $q$ -commute.
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