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Nonstandard Drinfeld-Sokolov reduction

F. Delduc·L. Feher·L. Gallot
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Abstract

Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet $(\A,Λ, d_1, d_0)$, where the $d_i$ are $\Z$-gradations of a loop algebra $\A$ and $Λ\in \A$ is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the $d_1$-grade zero part of $\A$ into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.

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BibTeXRIS

F. Delduc, L. Feher, L. Gallot. 1997-08-07. Nonstandard Drinfeld-Sokolov reduction. https://doi.org/10.1088/0305-4470%2F31%2F25%2F006

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