Equivariant Yoneda-center conjecture for symplectic duality

Let $\mathfrak{M}$ and $\mathfrak{M}^!$ be a symplectic dual pair, let $E$ be the Yoneda algebra of the category $\mathcal{O}$ for $\mathfrak{M}$, and let $\widetilde E$ be its universal deformation. Equivariant Yoneda-center conjecture. The graded ring

$$Z(\widetilde E)\cong H^*_{\mathbb{T}}(\mathfrak{M};\mathbb{C}).$$

This extends the Yoneda-center conjecture to the universal deformation and relates the center to equivariant cohomology; it remains open in general.