Singular localization for Quantum groups at generic $q$ - Backelin, E; Kremnizer, K (2011)
We quantize parabolic flag manifolds and describe categories of equivariant quantum $\D$-modules on them at a singular central character. We compute global sections at any $q \in \C^*$ and we also prove a singular version of Beilinson-Bernstein localization for a quantized enveloping algebra $\Uq(\g)$, when $q$ is generic.