Schur--Weyl Equivalences for Wreath Product Superalgebras

Let $A$ be an associative superalgebra over a field of characteristic zero. Let $n\ge d+1$. The main result of the paper establishes an equivalence of categories between supermodules for the wreath product $S_d\wr A$ and an explicitly defined category of supermodules for the general linear Lie algebra ${\mathfrak{g}\mathfrak{l}}_n(A)$. We also give an example showing the bound $n\ge d+1$ cannot be improved.