Tensor modules over Witt superalgebras

Abstract

In this paper, we study the tensor module P ⊗ M over the Witt superalgebra W + (resp. Wm,n), where P is a simple module over the Weyl superalgebra K + (resp. Km,n) and M is a simple weight module over the general linear Lie superalgebra $$\mathfrak{g}\mathfrak{l}\left( {m,n} \right)$$ . We obtain the necessary and sufficient conditions for P ⊗ M to be simple, and determine all the simple subquotients of P ⊗ M when it is not simple. All the work leads to the completion of some classification problems on the weight representation theories of W + and Wm,n.