  We study the Gaberdiel-Goddard spaces of systems of correlation functions
attached to an affine Kac-Moody Lie algebra $\gh$. We prove that these spaces
are isomorphic to the spaces of coinvariants with respect to certain
subalgebras of $\gh$. This allows to describe the Gaberdiel-Goddard spaces as
direct sums of tensor products of irreducible $\g$-modules with multiplicities
given by fusion coefficients. We thus reprove and generalize Frenkel-Zhu's
theorem.
