Tensor modules over Witt superalgebras

In this paper, we study the tensor module P ⊗ M over the Witt superalgebra W m,n + (resp. W m,n ), where P is a simple module over the Weyl superalgebra K m,n + (resp. K m,n ) and M is a simple weight module over the general linear Lie superalgebra 𝔤𝔩( m,n) . 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 m,n + and W m,n .