Module structure on $U(\mathfrak{h})$ for Kac-Moody algebras

Yan-an Cai, Haijun Tan, Kaiming Zhao

Let $\g$ be an arbitrary Kac-Moody algebra with a Cartan sualgebra $\h$. In this paper, we determine the category of $\g$-modules that are free $U(\h)$-modules of rank 1.