Vogan's quantization conjecture for nilpotent covers

Let $G$ be a complex reductive algebraic group and let $\mathfrak{g}=\operatorname{Lie}(G)$. Let $\widetilde{\mathcal{O}}$ be a finite connected cover of a nilpotent co-adjoint $G$-orbit.

Vogan's quantization conjecture. For each such cover $\widetilde{\mathcal{O}}$, there is a canonically defined completely prime primitive ideal $I_0(\widetilde{\mathcal{O}})$ in the universal enveloping algebra $U(\mathfrak{g})$.

The properties of these ideals and their relation to the covers are part of the quantization problem for nilpotent covers. They are intended to define unipotent representations, which are closely related to the classification of unitary representations; the supplied text does not establish whether the conjecture is resolved.