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arXiv · hep-th/9311161

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

B. Enriquez
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Abstract

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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B. Enriquez. 1993-11-28. Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction. https://doi.org/10.1007/bf01102201

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