2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76673We prove the decomposition conjecture of Leclerc and Thibon for the Schur algebra. We also give a new approach to the Lusztig conjecture for the dimension of the simple U(sl_k)-modules at roots of unity via canonical bases of the Hall algebra.AMS-tex, 30 pagesQuantum Algebratext