Two character formulas for $\widehat{s{l}_2}$ spaces of coinvariants

Abstract

We consider $\widehat{s{l}_2}$ spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra $U(sl_2\otimes\C[t])$. The first one is generated by $s{l}_2\otimes t^N$, and the second one is generated by $e\otimes P(t),f\otimes R(t)$ where $P(t),R(t)$ 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 $s{l}_3$-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors.

LaTeX, 22 pages; very minor changes

References in corpus (2)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Fermionic formulas for level-restricted generalized Kostka polynomials and coset branching functions

Cited by in corpus (1)

• A monomial basis for the Virasoro minimal series M(p,p') : the case 1<p'/p<2