Morita super-equivalence conjecture for reduced enveloping superalgebras

Let $\mathfrak{g}$ be a restricted Lie superalgebra, let $\chi\in\mathfrak{g}_{\bar{0}}^*$ be a $p$-character with Jordan decomposition $\chi=\chi_s+\chi_n$, and let

$$b_i=\text{dim}\mathfrak{g}_i-\text{dim}\mathfrak{g}_{\chi_s,i}\qquad (i\in\mathbb Z_2).$$

Write $U_\chi(\mathfrak{g})$ for the reduced enveloping superalgebra and let $\operatorname{Irr}(A)$ denote the isoclasses of simple $A$-supermodules. Morita super-equivalence conjecture. There are adjoint exact functors $F$ and $G$ between $U_\chi(\mathfrak{g})$-$\mathfrak{mod}$ and $U_\chi(\mathfrak{g}_{\chi_s})$-$\mathfrak{mod}$ such that, if $b_1$ is even, they are inverse equivalences, induce a type-preserving bijection between the two sets of simple modules, and

$$\text{dim} G(V)=p^{b_0/2}2^{b_1/2}\text{dim} V.$$

If $b_1$ is odd, then

$$F\circ G\cong\operatorname{Id}\oplus\Pi,\qquad G\circ F\cong\operatorname{Id}\oplus\Pi,$$

where $\Pi$ is the parity-change functor; moreover, $F$ exchanges types $M$ and $Q$, and for a simple module $V$ of type $M$ or $Q$, respectively,

$$\text{dim} G(V)=p^{b_0/2}2^{(b_1+1)/2}\text{dim} V$$

and

$$\text{dim} G(V)=p^{b_0/2}2^{(b_1-1)/2}\text{dim} V.$$

This conjecture predicts a precise categorical and dimensional relation between reduced enveloping superalgebras at a $p$-character and at its semisimple centralizer. The source presents it as a conjecture and does not provide a resolution in general.