Pauli-like principle for Abelian and non-Abelian FQHE quasiparticles

A general formulation of condensed matter physics describes the Hamiltonian as $H_0 + H_1$, where $H_0$ is a positive ``topological'' Hamiltonian with a highly-degenerate zero-energy ground state (extensive $T=0$ entropy) and $H_1$ is the ``physical'' Hamiltonian that splits this huge multiplet. Usually, $H_0$ is a non-interacting Hamiltonian, with zero modes that form a simple Fock space spanned by Wannier orbitals of low-energy electron bands, or a Landau level, etc. Systems of Laughlin FQHE quasiholes are described by a more general $H_0$ that removes low-relative-angular momentum two-particle states from the zero-mode spectrum, and the non-Abelian Moore-Read and Read-Rezayi quasihole systems involve removal of $n > 2$ particle states. The latter are candidates systems for topological quantum computation. The zero-modes count has been previously obtained by counting the number of linearly-independent polynomials of various types. I give a simpler Pauli-principle-like formulation that transparently gives the counting rules, and allows the creation of subsets of lowest-Landau-level Slater determinant states from which the zero-mode states can be constructed. This aids numerical diagonalization of $P_0H_1P_0$, where $P_0$ is the projection into the zero-modes space of $H_0$, for exact-diagonalization simulations of the manipulations of non-Abelian quasiparticles proposed for topological quantum computations.