Zk(r)-algebras, FQH ground states, and invariants of binary forms

A prominent class of model FQH ground states is those realized as correlation function of Z_k^(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 (z_2k) » ∏_i<j^{(z_i -z_j) 2 r / k} is devised. We provide some evidence that, at least when r = 2, our proposed Hamiltonian realizes Z_k⁽²⁾-wavefunctions as a unique ground state.