Сью Като: A homological realization of level-restricted Kostka polynomials

ABSTRACT: We explain that an integrable highest wight module of an affine Lie algebra admits a natural filtration from a view-point of representation theory of current algebras. This leads to an interpretation of level-restricted Kostka polynomials as the graded dimension of the space of conformal coinvariants, generalizing a result of B.Feigin-E.Feigin. Our interpretation also naturally realize global Weyl modules of current algebras of type $\mathsf{ADE}$ in terms of Schubert manifolds of thick affine Grassmanian, as predicted by Boris Feigin.

This talk is based on a joint work with Sergey Loktev