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Spaces of coinvariants and fusion product II. Affine sl_2 character formulas in terms of Kostka polynomials

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

In this paper, we continue our study of the Hilbert polynomials of coinvariants begun in our previous work math.QA/0205324 (paper I). We describe the sl_n-fusion products for symmetric tensor representations following the method of Feigin and Feigin, and show that their Hilbert polynomials are A_{n-1}-supernomials. We identify the fusion product of arbitrary irreducible sl_n-modules with the fusion product of their resctriction to sl_{n-1}. Then using the equivalence theorem from paper I and the results above for sl_3, we give a fermionic formula for the Hilbert polynomials of a class of affine sl_2-coinvariants in terms of the level-restricted Kostka polynomials. The coinvariants under consideration are a generalization of the coinvariants studied in [FKLMM]. Our formula differs from the fermionic formula established in [FKLMM] and implies the alternating sum formula conjectured in [FL] for this case.

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B. Feigin, M. Jimbo, R. Kedem, S. Loktev, T. Miwa. 2002-10-08. Spaces of coinvariants and fusion product II. Affine sl_2 character formulas in terms of Kostka polynomials. https://arxiv.org/abs/math/0208156

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