Cohomology in singular blocks of parabolic category $\mathcal{O}$

Abstract

We determine the dimensions of $\mathrm{Ext}$-groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category $\mathcal{O}$ for complex semisimple Lie algebras and affine Kac-Moody algebras.

arXiv comment14 pages. Minor revisions after a referee report. To appear in Glasg. Math. J