Capture-Recapture Models
We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU (2) 0 WZNW model. These have a form almost identical to that found in the c = -2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU (2) 0 W -algebras exactly reduce to those found in c = -2. We explicitly find the free field representations for the chiral j = 2 and j = 3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j = 2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.