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

Georgia Benkart, Seok-Jin Kang, Hyeonmi Lee +2

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…