Kac-Moody Groups and Integrability of Soliton Equations

Details Kac-Moody Groups and Integrability of Soliton Equations Kac-Moody Groups and Integrability of Soliton Equations

1993-11-29

arxiv.org/abs/hep-th/9311171v3

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, AMSLatex; extended version accepted for publication in Invent. Math

Scientific paper

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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