Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras

Details Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras

1997-03-31

arxiv.org/abs/solv-int/9704002v1

Physics

High Energy Physics

High Energy Physics - Theory

plain TeX, 12 pages

Scientific paper

10.1088/0305-4470/30/16/022

The Drinfeld-Sokolov reduction method has been used to associate with $gl_n$ extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps, implementing reduction of $gl_n$ to classical Lie algebras of type $B, C, D$, are here presented. Modifications corresponding, in the first place to factorisation of the Lax operator, and then to Wakimoto realisations of the current algebra components of the factorisation, are also described.

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