Level-rank duality of WZW models in conformal field theory

We consider the decomposition of the conformal blocks under the conformal embeddings. The case gl(lr)1containssl(l)rxsl(r)lxa a is an affine extension of the abelian subalgebra of the central elements of gl(lr)) is studied in detail. The reciprocal decompositions of gl(lr)1-modules induce a pairing between the spaces of conformal blocks of sl(l)r and sl(r)l Wess-Zumino-Witten models on the Riemann sphere. The completeness of the pairing is shown. Hence it defines a duality between two spaces. (orig.)