An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras - Qin, Fan (Symmetry, Integrability and Geometry: Methods and Applications, 2020)
Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the dual canonical bases of quantum unipotent subgroups. It also applies to the -analogs of -characters of simple modules of quantum affine algebras.