Singular localization for Quantum groups at generic $q$

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.

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