Parafermionic quasi-particle basis and fermionic-type characters Original Research Article

A quasi-particle basis of states for highest-weight modules in Zk parafermionic conformal theories is displayed. It is formulated in terms of an effective exclusion principle constraining strings of k fundamental parafermionic modes. The states of a module are then built by a simple filling process, with no singular-vector subtractions. That results in fermionic-sum representations of the characters, which are exactly the Lepowsky–Primc expressions. We also stress that the underlying combinatorics—which is the one pertaining to the Andrews–Gordon identities—has a remarkably natural parafermionic interpretation.