The Polynomial Behavior of Weight Multiplicities for the Affine KacMoody Algebras $A^{(1)}_r$
Abstract
We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine KacMoody algebra $A_{r}^{(1)}$ is a polynomial in the rank $r$. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.math/9809026
 arXiv:
 arXiv:math/9809026
 Bibcode:
 1998math......9026B
 Keywords:

 Mathematics  Representation Theory;
 17B67;
 17B65
 EPrint:
 29 pages