Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus

Details Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus

2007-07-04

arxiv.org/abs/0707.0659v1

Mathematics

Representation Theory

Scientific paper

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.

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