Coadjoint Orbits of the Generalised Sl(2) Sl(3) Kdv Hierarchies

Details Coadjoint Orbits of the Generalised Sl(2) Sl(3) Kdv Hierarchies Coadjoint Orbits of the Generalised Sl(2) Sl(3) Kdv Hierarchies

1991-10-09

arxiv.org/abs/hep-th/9110025v1

Nucl.Phys. B379 (1992) 340-376

Physics

High Energy Physics

High Energy Physics - Theory

37 pages

Scientific paper

10.1016/0550-3213(92)90600-G

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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