Shen-Larsson’s modules for simple generalized Witt algebras

In this paper, we extend the Shen-Larsson’s construction for Witt algebras to simple generalized Witt algebras and construct a class of modules for these algebras. We determine the irreducibility and isomorphism of these modules under certain countability conditions. Thus we obtain a large family of irreducible weight modules other than highest weight modules and many irreducible non-weight modules over the simple generalized Witt algebras.