PreprintDifferential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torusYuly Billig, Alexander Molev and Ruibin ZhangAbstractWe study irreducible representations for the Lie algebra of vector fields on a 2dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the Lie algebra of vector fields. We prove this result by studying vertex algebras associated with the Lie algebra of vector fields on a torus and solving noncommutative differential equations that we derive using the vertex algebra technique. This paper is available as a pdf (264kB) file.
