Decomposition of sl2^,k⊕sl2^,1 Highest Weight Representations for Generic Level k and Equivalence Between Two-Dimensional CFT Models

We construct highest weight vectors of sl2^,k+1⊕Vir in tensor products of highest weight modules of sl2^,k and sl2^,1, and thus for generic weights we find the decomposition of the tensor product into irreducibles of sl2^k+1⊕Vir. The construction uses Wakimoto representations of sl2^,k, but the obtained vectors can be mapped back to Verma modules. Singularities of this mapping are cancelled by a renormalization. A detailed study of “degenerations” of Wakimoto modules allowed to find the renormalization factor explicitly. The obtained result is a significant step forward in a proof of equivalence of certain two-dimensional CFT models.