  We discuss $w_\infty$ and $sl_q(2)$ 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 $w_\infty$ and two $sl_q(2)$
algebras, instead of one set each discussed in the literature. The general
wavefunctions for the Landau problem with rational total flux is also
presented.
