The structure of ground states of generic FQH states on a torus is studied by using both effective theory and electron wavefunction. The relation between the effective theory and the wavefunction becomes transparent when one considers the ground state structure. We find that the non-abelian Berry’s phases of the abelian Hall states generated by twisting the mass matrix are identical to the modular transformation matrix for the characters of Gaussian conformal field theory. We also show that the Haldane-Rezayi spin singlet state has a ten fold ground state degeneracy on a torus which indicates such a state is a non-abelian Hall state.
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A 1993 study studied this question.