The Zk(su(2),3/2) parafermions

We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 32(1−1k), with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The spectrum of the completely reducible representations is also determined. The primary fields turns out to be labeled by two positive integers instead of a single one for the usual parafermionic models. The simplest singular vectors are also displayed. It is argued that these models are equivalent to the non-unitary minimal Wk(k+1,k+3) models. More generally, we expect all Wk(k+1,k+2β) models to be identified with generalized parafermionic models whose lowest-dimensional parafermion has dimension β(1−1/k).