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:
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arXiv Mathematics e-prints
- Pub Date:
- December 2002
- DOI:
- 10.48550/arXiv.math/0212347
- arXiv:
- arXiv:math/0212347
- Bibcode:
- 2002math.....12347F
- Keywords:
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- Quantum Algebra
- E-Print:
- 30 pages