Irreducible Witt modules from Weyl modules and [formula omitted]-modules

Abstract

For an irreducible module P over the Weyl algebra Kn+ (resp. Kn) and an irreducible module M over the general linear Lie algebra gln, using Shen's monomorphism, we make P⊗M into a module over the Witt algebra Wn+ (resp. over Wn). We obtain the necessary and sufficient conditions for P⊗M to be an irreducible module over Wn+ (resp. Wn), and determine all submodules of P⊗M when it is reducible. Thus we have constructed a large family of irreducible weight modules with many different weight supports and many irreducible non-weight modules over Wn+ and Wn, including some known modules and many new modules.