Quantum Hall effect wavefunctions as cyclic representations of U_q(sl(2))

Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p + 1, 2/2p + 1...., 2p/2p + 1, 1, are shown to form a basis of irreducible cyclic representations of the quantum algebra U_q(sl(2)) at q^2p+1 = 1. Thus, the wavefunctions Ψ_P/Q possessing filling factors P/Q < 1 where Q is odd and P, Q are relatively prime integers are classified in terms of U_q(sl(2)).