2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27356We show that there exists quantum group symmetry $ sl_{q}(2) $ in the fractional quantum Hall effect (FQHE) and this symmetry governs the degeneracy of ground-state level. Under the periodic boundary condition, the degeneracy of the ground state is related to the cyclic representation of SL_q(2). We also discuss the influence of impurity.Preprint ( reprint ) of Nankai Institute of Mathematics. Submitted to Phys. Rev. B. To request a hard copy, write to Prof. Mo-lin Ge, Director of Nankai Institute of Mathematics. Do not send emails to this computer accountCondensed Mattertext