New irreducible weight modules over Witt algebras with infinite-dimensional weight spaces

liu, genqiang; zhao, kaiming;

Let d > 1 be an integer. In 1986, Shen defined a class of weight modules Fα b (V) over the Witt algebra Wd for α ∈ Cd, b ∈ C, and an irreducible module V over the general linear Lie algebra gld on which the identity matrix acts as multiplication by b. In 1996, Eswara Rao determined necessary and sufficient conditions for these modules to be irreducible when V is finite-dimensional. In this note, we will determine necessary and sufficient conditions for all these modules Fα b (V ) to be irreducible where V is not necessarily finite-dimensional. In this
way, we obtain a large new family of irreducible Wd-modules with infinite-dimensional weight spaces.