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-dim…