Unique factorization conjecture for indecomposable dual canonical basis elements

Let $B^*$ be the dual canonical basis of the quantum matrix algebra $O_q(M(n))$. Call $b\in B^*$ decomposable if there exist $m\in\mathbb Z$ and $b_1,b_2\in B^*$ such that $b=q^m b_1b_2$, and call it indecomposable otherwise. By repeated decomposition, every basis element can be written as

$$b=q^m b_1b_2\cdots b_s$$

for some $m\in\mathbb Z$ and indecomposable $b_1,\ldots,b_s\in B^*$. Unique factorization conjecture. The decomposition is unique up to a permutation of the indecomposable factors. This asserts a unique factorization property for dual canonical basis elements; the supplied text gives no resolution or further context establishing the claim.