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

Billig, Yuly; Molev, Alexander; Zhang, Ruibin

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

Authors

Billig, Yuly

Molev, Alexander

Zhang, Ruibin

Description

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.