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We construct a filtration on integrable highest weight module of an affineLie algebra whose adjoint graded quotient is a direct sum of global Weylmodules. We show that the graded multiplicity of each Weyl module there isgiven by a corresponding level-restricted Kostka polynomial. This leads to aninterpretation of level-restricted Kostka polynomials as the graded dimensionof the space of conformal coinvariants. In addition, as an application of thelevel one case of the main result, we realize global Weyl modules of currentalgebras of type $\mathsf{ADE}$ in terms of Schubert manifolds of thick affineGrassmanian, as predicted by Boris Feigin.

A Weyl Module Stratification of Integrable Representations (with an appendix by Ryosuke Kodera)