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

Abstract

The Drinfeld-Sokolov reduction method has been used to associate with $g{l}_n$ extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps, implementing reduction of $g{l}_n$ 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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References in corpus (6)

• Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies
• On the constrained KP hierarchy
• Constrained KP Models as Integrable Matrix Hierarchies
• Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
• On the generalized Miura transformation
• An explicit construction of Wakimoto realizations of current algebras