Lusztig's isomorphism conjecture for quiver mutations

Let $T_i$ denote the Lusztig isomorphisms associated with the simple roots of the quantum group, and let quiver mutations act on the corresponding quantum cluster structure. Lusztig's isomorphism conjecture. The Lusztig's isomorphisms $T_i$ are represented by a sequence of quiver mutations. This would provide the mutation-theoretic realization needed for the symmetry of the cluster structure and connect Lusztig's transformations with the quantum cluster algebra framework; the source presents this assertion as a conjecture without stating a resolution.