The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A^{(1)}_r$

Details The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A^{(1)}_r$ The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A^{(1)}_r$

1998-09-06

arxiv.org/abs/math/9809026v1

Mathematics

Representation Theory

29 pages

Scientific paper

We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody 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.

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