  We show that the quantum Hall wave functions for the ground states in the
Jain series can be exactly expressed in terms of correlation functions of local
vertex operators, V_n, corresponding to composite fermions in the n:th
composite-fermion (CF) Landau level. This allows for the powerful mathematics
of conformal field theory to be applied to the successful CF phenomenology.
Quasiparticle and quasihole states are expressed as correlators of anyonic
operators with fractional (local) charge, allowing a simple algebraic
understanding of their topological properties that are not manifest in the CF
wave functions.
