Loop Algebra Moment Maps and Hamiltonian Models for the Painleve Transcendants

The isomonodromic deformations underlying the Painlevé transcendants are interpreted as nonautonomous Hamiltonian systems in the dual \(\gR^*\) of a loop algebra \(\tilde\grg\) in the classical \(R\)-matrix framework. It is shown how canonical coordinates on symplectic vector spaces of dimensions fo...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Harnad, J, M -A Wisse
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.05.1993
Subjects
Deformation
Hamiltonian functions
Mathematical analysis
Matrix methods
Vector spaces
Online AccessGet full text

Cover

More Information
Summary:The isomonodromic deformations underlying the Painlevé transcendants are interpreted as nonautonomous Hamiltonian systems in the dual \(\gR^*\) of a loop algebra \(\tilde\grg\) 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 \(\gR^*\) via a moment map embedding. The Hamiltonians underlying the Painlevé transcendants are obtained by pulling back elements of the ring of spectral invariants. These are shown to determine simple Hamiltonian systems within the underlying symplectic vector space.
ISSN:2331-8422