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Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials

B. Feigin·M. Jimbo·R. Kedem·S. Loktev·T. Miwa
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Abstract

The fusion rule gives the dimensions of spaces of conformal blocks in the WZW theory. We prove a dimension formula similar to the fusion rulefor spaces of coinvariants of affine Lie algebras g^. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weight g^-modules and tensor products of finite-dimensional evaluation representations of g\otimes\C[t]. In the sl_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.

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B. Feigin, M. Jimbo, R. Kedem, S. Loktev, T. Miwa. 2002-10-08. Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials. https://arxiv.org/abs/math/0205324

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