  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
representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the
wavefunctions \Psi_{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)). Adopted
as dynamical symmetry this leads to non--existence of a ``universal microscopic
theory" of the quantum Hall effect, defined as the eigenvalue problem of a
differential operator O: O \Psi_\nu =\ell_\nu \Psi_\nu. for \nu =1,1/3,2/3,...,
in the complex plane.
