Kac-Moody Groups and Integrability of Soliton Equations

Boris Feigin, Edward Frenkel

Published 1993-11-29, updated 1994-11-17Version 3

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.