Coadjoint Orbits of the Generalised Sl(2) Sl(3) Kdv Hierarchies
Nigel J. Burroughs
Abstract
In this paper we develop two coadjoint orbit constructions for the phase spaces of the generalised Sl(2) and Sl(3) KdV hierachies. This involves the construction of two group actions in terms of Yang Baxter operators, and an Hamiltonian reduction of the coadjoint orbits. The Poisson brackets are reproduced by the Kirillov construction. From this construction we obtain a `natural' gauge fixing proceedure for the generalised hierarchies.
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