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We discuss $w_\infty$ and $sl_q(2)$ symmetries in Chern-Simons theory andLandau problem on a torus. It is shown that when the coefficient of theChern-Simons term, or when the total flux passing through the torus is arational number, there exist in general two $w_\infty$ and two $sl_q(2)$algebras, instead of one set each discussed in the literature. The generalwavefunctions for the Landau problem with rational total flux is alsopresented.Comment: 12 pages. Plain Tex

W∞ AND SLq(2) ALGEBRAS IN THE LANDAU PROBLEM AND CHERN-SIMONS THEORY ON A TORUS

W_∞ AND SL_q(2) ALGEBRAS IN THE LANDAU PROBLEM AND CHERN-SIMONS THEORY ON A TORUS