Hamiltonian reductions in Matrix Painlevé systems

Abstract

For certain finite groups $G$ of Bäcklund transformations we show that the dynamics of $G$-invariant configurations of $n|G|$ Calogero--Painlevé particles is equivalent to certain $n$-particle Calogero--Painlevé system. We also show that the reduction of dynamics on $G$-invariant subset of $n|G|\times n|G|$ matrix Painlevé system is equivalent to certain $n\times n$ matrix Painlevé system. The groups $G$ correspond to folding transformations of Painlevé equations. The proofs are based on the Hamiltonian reductions.

37 pages

References in corpus (1)

• Noncommutative Painlevé equations and systems of Calogero type