fusion rule gives the dimensions of spaces of conformal blocks in Wess-Zumino-Witten (WZW) theory. We prove a dimension formula similar to the fusion rule for spaces of coinvariants of affine Lie algebras (g) over cap. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weight (g) over cap -modules and tensor products of finite-dimensional evaluation representations of g circle times C[t].
In the (sl) over cap (2)-case we prove that their associated graded spaces are isomorphic to the spaces of coinvariants of fusion products and that their Hilbert polynomials are the level-restricted Kostka polynomials.