Degeneracy of the lowest Landau level and quantum group U-q(sl(2)) on the sphere

We show that the degree of degeneracy of a one-electron system on the surfa ce of a sphere, in the lowest Landau level, can be obtained in a consistent way using the cyclic irreducible representation of the quantum group U-q ( sl(2)). The allowed degree of degeneracy arises naturally from the properti es of this representation when q is a root of unity.