Gauge Modules for the Lie Algebras of Vector Fields on Affine Varieties

Journal article, 2021

For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra A of functions and the Lie algebra V of vector fields on the variety. We prove that a gauge module corresponding to a simple glN-module is irreducible as a module over the Lie algebra of vector fields unless it appears in the de Rham complex.