  We study multiplicative properties of the (quantum) dual canonical basis B*
associated to a semi-simple complex Lie group G. We provide a subset D of B*
such that the following property holds : if two elements b, b' in B* q-commute
and if one of these elements is in D, then the product bb' is in B* up to a
power of q, where q the quantum parameter. If G is SL_n, then D is the set of
so-called quantum flag minors and we obtain a generalization of a result of
Leclerc-Nazarov-Thibon, see ArXiv:Math.QA/0011074.
