A weight-formula for all highest weight modules, and a higher order parabolic category $\mathcal{O}$

Apoorva Khare, G. Krishna Teja

Let $\mathfrak{g}$ be a complex Kac-Moody algebra, with Cartan subalgebra $\mathfrak{h}$. Also fix a weight $\hat{I}»\in {\mathfrak{h}}^{\ast }$. For $M(\hat{I}»)\twoheadrightarrow V$ an arbitrary high…