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

We determine the dimensions of $\mathrm{E}\mathrm{x}\mathrm{t}$-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.