Irreducible Modules for the Lie Algebra of Divergence Zero Vector Fields on a Torus

This article investigates the irreducibility of certain representations for the Lie algebra of divergence zero vector fields on a torus. In [2] Rao constructs modules for the Lie algebra of polynomial vector fields on an N-dimensional torus, and determines the conditions for irreducibility. The current article considers the restriction of these modules to the subalgebra of divergence zero vector fields. It is shown here that Rao's results transfer to similar irreducibility conditions for the Lie algebra of divergence zero vector fields.