Fermionic formulas for (k, 3)-admissible configurations

Details Fermionic formulas for (k, 3)-admissible configurations Fermionic formulas for (k, 3)-admissible configurations

2002-12-27

arxiv.org/abs/math/0212347v1

Mathematics

Quantum Algebra

30 pages

Scientific paper

We obtain the fermionic formulas for the characters of (k, r)-admissible configurations in the case of r=2 and r=3. This combinatorial object appears as a label of a basis of certain subspace $W(\Lambda)$ of level-$k$ integrable highest weight module of $\hat{sl}_{r}$. The dual space of $W(\Lambda)$ is embedded into the space of symmetric polynomials. We introduce a filtration on this space and determine the components of the associated graded space explicitly by using vertex operators. This implies a fermionic formula for the character of $W(\Lambda)$.

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