FUSION AND BRAIDING IN W-ALGEBRA EXTENDED CONFORMAL THEORIES

We define the chiral conformal blocks of integer-spin extended (W-algebra) conformal theories by the fusion of elementary ones. The braid group representation matrices which realize the exchange algebra are computed. They are shown to coincide with the Boltzmann weights - in a certain limit of the spectral parameter - of the critical face models of Jimbo et al. In the unitary cases, where the extended conformal theories can be realized as cosets g ̂k ⊕ g ̂1/ g ̂k+1, we relate the braiding matrices of the former to those of the ĝ WZW models. In this article we restrict ourselves to the case corresponding to symmetric tensor representations of An. © 1990.