Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction. (English) Zbl 0833.35123

Theor. Math. Phys. 98, No. 3, 256-258 (1994) and Teor. Mat. Fiz. 98, No. 3, 375-378 (1994).
Summary: 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 \(\widehat N_+/A\), with \(\widehat N_+\) affine nilpotent and \(A\) the 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 \(\text{sl}_2\) case.


35Q53 KdV equations (Korteweg-de Vries equations)
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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