Clustering in quantum Hall wavefunctions and conformal field theory amplitudes

We consider lowest Landau level wavefunctions for bosons subjected to a magnetic field in the plane. We study the zero-energy eigenstates of a projection Hamiltonian which forbids three particles to come together with relative angular momentum less than six and, in addition, forbids one of two linearly-independent states of relative angular momentum six. The counting of edge excitations of this Hamiltonian agrees with the character formula for the N=1 superconformal Kac vacuum module at generic central charge c. This Hamiltonian is expected to be gapless for all c. For particular c, we try to ``improve'' the Hamiltonian by adding additional terms (related to singular vectors in the modules), so as to obtain a rational theory. We consider specifically states whose wavefunctions are related to the M(8,3) and tricritical Ising CFTs.