Cells in quantum affine sl_n

We study Lusztig’s theory of cells for quantum affine ${\mathfrak{s}\mathfrak{l}}_n$. 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.