  The Z_k-parafermion Hall state is an incompressible fluid of k-electron
clusters generalizing the Pfaffian state of paired electrons. Extending our
earlier analysis of the Pfaffian, we introduce two ``parent'' abelian Hall
states which reduce to the parafermion state by projecting out some neutral
degrees of freedom. The first abelian state is a generalized (331) state which
describes clustering of k distinguishable electrons and reproduces the
parafermion state upon symmetrization over the electron coordinates. This
description yields simple expressions for the quasi-particle wave functions of
the parafermion state. The second abelian state is realized by a conformal
theory with a (2k-1)-dimensional chiral charge lattice and it reduces to the
Z_k-parafermion state via the coset construction su(k)_1+su(k)_1/su(k)_2. The
detailed study of this construction provides us a complete account of the
excitations of the parafermion Hall state, including the field identifications,
the Z_k symmetry and the partition function.

High Energy Physics - Theory;Mesoscale and Nanoscale Physics