We discuss ω∞ and slq(2) symmetries in Chern-Simons theory and Landau problem on a torus. It is shown that when the coefficient of the Chern-Simons term, or when the total flux passing through the torus is a rational number, there exist in general two w∞ and slq(2) algebras, instead of one set each discussed in the literature. The general wave functions for the Landau problem with rational total flux is also presented.