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 ⊗ tN, 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 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.
- Publication:
-
International Journal of Modern Physics A
- Pub Date:
- 2004
- DOI:
- 10.1142/S0217751X04020361
- arXiv:
- arXiv:math/0211354
- Bibcode:
- 2004IJMPA..19S.134F
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory
- E-Print:
- LaTeX, 22 pages