Fermionic formulas for (k, 3)admissible configurations
Abstract
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 $W(\Lambda)$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2002
 DOI:
 10.48550/arXiv.math/0212347
 arXiv:
 arXiv:math/0212347
 Bibcode:
 2002math.....12347F
 Keywords:

 Quantum Algebra
 EPrint:
 30 pages