# Dual isomonodromic deformations and moment maps to loop algebras

@article{Harnad1993DualID,
title={Dual isomonodromic deformations and moment maps to loop algebras},
journal={Communications in Mathematical Physics},
year={1993},
volume={166},
pages={337-365}
}
• Published 18 January 1993
• Mathematics
• Communications in Mathematical Physics
The Hamiltonian structure of the monodromy preserving deformation equations of Jimboet al [JMMS] is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop algebras. The nonautonomous Hamiltonian systems generating the deformations are obtained by pulling back spectral invariants on Poisson subspaces consisting of elements that are rational in the loop parameter and identifying the deformation parameters with those…
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Here I = S j (a2j 1,a2j) andI(y) is the characteristic function of the set I. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in I is equal to �(a). Also �(a) is a