O ct 2 00 2 SPACES OF COINVARIANTS AND FUSION PRODUCT II . ŝl 2 CHARACTER FORMULAS IN TERMS OF KOSTKA

In this paper, we continue our study of the Hilbert poly-nomials of coinvariants begun in our previous work [FJKLM] (paper I). We describe the sln fusion products for symmetric tensor representations following the method of [FF], and show that their Hilbert polynomials are An−1-supernomials. We identify the fusion product of arbitrary ir-reducible sln-modules with the fusion product of their resctriction to sln−1. Then using the equivalence theorem from paper I and the results above for sl3 we give a fermionic formula for the Hilbert polynomials of a class of sl2 coinvariants in terms of the level-restricted Kostka poly-nomials. 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.