2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64862We study Lusztig's theory of cells for quantum affine $\mathfrak{sl}_n$. Using the geometric construction of the quantum group due to Lusztig and Ginzburg--Vasserot, we describe explicitly the two-sided cells, the number of left cells in a two--sided cell, and the asymptotic algebra, verifying conjectures of Lusztig.Quantum AlgebraRepresentation Theorytext