Irreducible jet modules for the vector field Lie algebra on

Abstract

For a commutative algebra A over denote A module over the smash product is called a jet -module, where is the universal enveloping algebra of In the present paper, we study jet modules in the case of We show that where is the Weyl algebra and L is a Lie subalgebra of called the jet Lie algebra corresponding to Using a Lie algebra isomorphism where is the subalgebra of vector fields vanishing at the point (1, 0), we show that any irreducible finite dimensional L-module is isomorphic to an irreducible -module. As an application, we give tensor product realizations of irreducible jet modules over with uniformly bounded weight spaces.