CLASSIFICATION OF SIMPLE BOUNDED WEIGHT MODULES OF THE LIE ALGEBRA OF VECTOR FIELDS ON Cn

Let W-n(+) be the Lie algebra of vector fields on C-n. In this paper, we classify all simple bounded weight W-n(+) modules. Any such module is isomorphic to the simple quotient of a tensor module F(P, M) = P circle times M for a simple weight module P over the Weyl algebra K-n(+) = C[t(1), . . . , t(n), partial derivative/partial derivative t(1), . . . , partial derivative/partial derivative t(n)] and a finite-dimensional simple gl(n) (C) module M.

Automated summary

In this paper, we classify the simple bounded weight modules of the Lie algebra of vector fields on C-n. The classification result shows that any simple bounded weight module is isomorphic to the simple quotient of a tensor module F(P, M), where P is a simple weight module over the Weyl algebra and M is a finite-dimensional simple gl(n) (C) module.