%0 Journal Article
%T Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus
%A Yuly Billig
%A Alexander Molev
%A Ruibin Zhang
%J Mathematics
%D 2007
%I arXiv
%X We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional 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 non-commutative differential equations that we derive using the vertex algebra technique.
%U http://arxiv.org/abs/0707.0659v1