Simplicity conjecture for canonical quantizations

Let $X$ be a conical symplectic singularity, and let $\cA_0$ denote the canonical quantization of $\CC[X]$.

Simplicity conjecture. The algebra $\cA_0$ is simple.

Canonical quantizations arise from the zero point in the parameter space of filtered quantizations. Simplicity would imply that all Harish-Chandra bimodules over these quantizations have full support; the paper gathers evidence but does not resolve the conjecture in general.