A prominent class of model FQH ground states is those realized as correlation function of Zk(r)-algebras. In this paper, we study the interplay between these algebras and their corresponding wavefunctions. In the hopes of realizing these wavefunctions as a unique densest zero energy state, we propose a generalization for the projection Hamiltonians. Finally, using techniques from invariants of binary forms, an ansatz for computation of correlations « ψ (z1) ⋯ ψ (z2k) » ∏i<j(zi -zj) 2 r / k is devised. We provide some evidence that, at least when r = 2, our proposed Hamiltonian realizes Zk(2)-wavefunctions as a unique ground state.