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Two Character Formulas for { {sl}}2 Spaces of Coinvariants

We consider ŝl2 spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra U(sl2 ⊗ C[t]). The first one is generated by sl2 ⊗ t N , and the second one is generated by e⊗ P (t), f ⊗ P (t) where P (t), P (t) are fixed generic polynomials. (We also treat a generalization of the latter.) Using a method developed in our previous paper, we give new fermionic formulas for their Hilbert polynomials in terms of the level-restricted Kostka polynomials and q-multinomial symbols. As a byproduct, we obtain a fermionic formula for the fusion product of sl3-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors.