Loop Algebra Moment Maps and Hamiltonian Models for the Painlevé Transcendants

@inproceedings{Harnad1993LoopAM,
  title={Loop Algebra Moment Maps and Hamiltonian Models for the Painlev{\'e} Transcendants},
  author={J. Harnad and M. A. Wisse},
  year={1993}
}
The isomonodromic deformations underlying the Painlevé transcendants are interpreted as nonautonomous Hamiltonian systems in the dual g̃R of a loop algebra g̃ in the classical R-matrix framework. It is shown how canonical coordinates on symplectic vector spaces of dimensions four or six parametrize certain rational coadjoint orbits in g̃R via a moment map embedding. The Hamiltonians underlying the Painlevé transcendants are obtained by pulling back elements of the ring of spectral invariants… CONTINUE READING