Degeneracy of Landau Level and Quantum Group SL_q(2)

Abstract

We show that there is a kind of quantum group symmetry $sl_{q}(2)$ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group $sl_{q}(2)$.Comment: 10 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE, Director of Nankai Institute of Mathematics. Do not send emails to this computer accoun