An extension of the KdV hierarchy arising from Weyl algebra representations of toroidal Lie algebras.

摘要

The construction of the Korteweg-de Vries (KdV) hierarchy of partial differential equations using the affine Lie algebra slˆ2 illustrates a remarkable connection between Lie algebras and partial differential equations. Recently Billig has extended this construction in two ways, first by using toroidal Lie algebras instead of affine algebras, and second by considering representations in a Weyl algebra. Here we combine these two methods to obtain a doubly extended hierarchy of partial differential equations.