  Recently, Jack polynomials have been proposed as natural generalizations of
Z_k Read-Rezayi states describing non-Abelian fractional quantum Hall systems.
These polynomials are conjectured to be related to correlation functions of a
class of W-conformal field theories based on the Lie algebra A_{k-1}. These
theories can be considered as non-unitary solutions of a more general series of
CFTs with Z_k symmetry, the parafermionic theories. Starting from the
observation that some parafermionic theories admit unitary solutions as well,
we show, by computing the corresponding correlation functions, that these
theories provide trial wavefunctions which satisfy the same clustering
properties as the non-unitary ones. We show explicitly that, although the
wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack
polynomial, they still show a fine structure where the mathematical properties
of the Jack polynomials play a major role.
