Two Character Formulas for ̂ { {sl}}_{2} Spaces of Coinvariants
Abstract
We consider ̂ { {sl}}_{2} spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra U({ {sl}}_{2} ⊗ {C}[t]). The first one is generated by {sl}_{2} ⊗ t^{N}, and the second one is generated by e⊗ P(t), f⊗ /line{P}(t) where P(t), /line{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 levelrestricted Kostka polynomials and qmultinomial 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 antisymmetric) tensors.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2004
 DOI:
 10.1142/S0217751X04020361
 arXiv:
 arXiv:math/0211354
 Bibcode:
 2004IJMPA..19S.134F
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 LaTeX, 22 pages