Kac-Moody Groups and Integrability of Soliton Equations

Boris Feigin; Edward Frenkel

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arXiv · hep-th/9311171

Kac-Moody Groups and Integrability of Soliton Equations

Boris Feigin·Edward Frenkel

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Abstract

A new approach to integrability of affine Toda field theories and closely related to them KdV hierarchies is proposed. The flows of a hierarchy are explicitly identified with infinitesimal action of the principal abelian subalgebra of the nilpotent part of the corresponding affine algebra on a homogeneous space. This is an extended version of the paper "Generalized KdV flows and nilpotent subgroups of affine Kac-Moody groups"; it has been accepted for publication in Inventiones Mathematicae.

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Boris Feigin, Edward Frenkel. 1994-11-17. Kac-Moody Groups and Integrability of Soliton Equations. https://arxiv.org/abs/hep-th/9311171

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