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Weight multiplicity polynomials for affne Kac-Moody algebras of type $A_n^{(1)}
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- Authors
- Issue Date
- 1996-11
- Publisher
- Springer Verlag
- Citation
- Compositio Math. 104 (1996) 153-187
- Abstract
- For the affine Kac--Moody algebras X_r^{(1)} it has been conjectured by Benkart and Kass that for fixe d dominant weights \lambda,\mu, the multiplicity of the weight \mu in the irreducible X_r^{(1)}-module L(\lambda) of highest wei ght \lambda is a polynomial in r which depends on the type X of the alg ebra. In this paper we provide a precise conjecture for the degree of that polynomial for the algebras A_r^{(1)}. To offer evidence for this conjecture we p rove it for all dominant weights \lambda and all weights \mu of depth \leqslant 2 by explicitly exhibiting the polynomials as expressions involving Kostka numbers.
- ISSN
- 0010-437X (Print)
1570-5846 (Online)
- Language
- English
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