The center conjecture for finite W-superalgebras

Let $\mathfrak{g}$ be the Lie superalgebra and $e$ the nilpotent element defining the finite $W$-superalgebra $U(\mathfrak{g},e)$. Let $Z(U(\mathfrak{g}))$ and $Z(U(\mathfrak{g},e))$ denote the centers of $U(\mathfrak{g})$ and $U(\mathfrak{g},e)$, respectively, and let

$$\operatorname{Pr}:Z(U(\mathfrak{g}))\longrightarrow Z(U(\mathfrak{g},e))$$

be the projection induced by $U(\mathfrak{g})\twoheadrightarrow U(\mathfrak{g})/I_\chi$. Center conjecture. The center of $U(\mathfrak{g},e)$ coincides with the image of $Z(U(\mathfrak{g}))$ under $\operatorname{Pr}$:

$$Z(U(\mathfrak{g},e))=\operatorname{Pr}\bigl(Z(U(\mathfrak{g}))\bigr).$$

For complex semisimple Lie algebras, the analogous projection is known to be an algebra isomorphism; the conjecture asks for the corresponding equality of centers in the finite W-superalgebra setting.