Two character formulas for $\hat{sl_2}$ spaces of coinvariants

Details Two character formulas for $\hat{sl_2}$ spaces of coinvariants Two character formulas for $\hat{sl_2}$ spaces of coinvariants

2002-11-22

arxiv.org/abs/math/0211354v2

Internat. J. Modern Phys. A 19 (2004), May suppl., 134-154

Mathematics

Quantum Algebra

LaTeX, 22 pages; very minor changes

Scientific paper

We consider $\hat{sl_2}$ 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 $sl_2\otimes t^N$, 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 $sl_3$-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors.

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