Schur--Weyl Equivalences for Wreath Product Superalgebras

Abstract

Let $A$ be an associative superalgebra over a field of characteristic zero. Let $n \geq d+1$. 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 $\mathfrak{gl}_{n}(A)$. We also give an example showing the bound $n \geq d+1$ cannot be improved.