Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction

Details Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction

1993-11-28

arxiv.org/abs/hep-th/9311161v1

Theor.Math.Phys. 98 (1994) 256-258; Teor.Mat.Fiz. 98N3 (1994) 375-378

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/BF01102201

We note that a version ``with spectral parameter'' of the Drinfeld-Sokolov reduction gives a natural mapping from the KdV phase space to the group of loops with values in $\widehat N_{+}/A, \widehat N_{+}$~: affine nilpotent and $A$ principal commutative (or anisotropic Cartan) subgroup~; this mapping is connected to the conserved densities of the hierarchy. We compute the Feigin-Frenkel action of $\widehat n_{+}$ (defined in terms of screening operators) on the conserved densities, in the $sl_2$ case.

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