FUSION POTENTIALS FOR G(K) AND HANDLE SQUASHING

Using Chern-Simons gauge theory, we show that the fusion ring of the conformal field theory G(k) (G any Lie algebra) is isomorphic to P[u]/(del V) where (del V) is the ideal generated by conditions delV = 0. We explicitly construct V for all G(k). We also derive a residue-like formula for the correlation functions in the Chern-Simons theory thus providing an RCFT version of the residue formula for the topological Landau-Ginzburg model. An operator that acts like a measure in this residue formula has the interpretation of a handle-squashing operator and explicit formulae for this operator are given.