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This article gives a complete account of the modular properties and Verlindeformula for conformal field theories based on the affine Kac-Moody algebrasl(2) at an arbitrary admissible level k. Starting from spectral flow and thestructure theory of relaxed highest weight modules, characters are computed andmodular transformations are derived for every irreducible admissible module.The culmination is the application of a continuous version of the Verlindeformula to deduce non-negative integer structure coefficients which areidentified with Grothendieck fusion coefficients. The Grothendieck fusion rulesare determined explicitly. These rules reproduce the well-known fusion rules ofKoh and Sorba, negative coefficients included, upon quotienting theGrothendieck fusion ring by a certain ideal.

Modular Data and Verlinde Formulae for Fractional Level WZW Models II