Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces

Abstract

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $su_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $su_q(2)$ algebra .