A translation principle for Kac-Moody algebras

Abstract:

Let $\mathfrak {g}$ be a Kac-Moody algebra defined by a symmetrizable generalized Cartan matrix. We show that the multiplicity of the irreducible module $L({w_1} \cdot \lambda )$ in the Verma module $M({w_2}\cdot \lambda )$ depends only on the elements ${w_1}$ and ${w_2}$ of the Weyl group, and not on the dominant integral weight $\lambda$, generalizing the translation principle of Jantzen for finite-dimensional algebras.