An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra

1997/06/18 by Billig, Yuly · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.solv-int/9706008

Abstract

In this article we show how to construct hierarchies of partial differential equations from the vertex operator representations of toroidal Lie algebras. In the smallest example - rank 2 toroidal cover of sl₂ - we obtain an extension of the KdV hierarchy. We use the action of the corresponding infinite-dimensional group to construct solutions for these non-linear PDEs.

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• Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras

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