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An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: Recent Developments

On Matrix Painleve Systems

Author: Yoshihiro Murata (Nagasaki University)


Reconstructing the reduction process of Anti-self-dual Yang-Mills equation to Painleve equations in Mason-Woodhouse's work, we can obtain matrix type ordinary differential equations MPS (Matrix Painleve Systems). MPS are characterized by Young diagrams of weight 4 and constant matrix P, and are classified into 15 types. 15 MPS are transformed into Painleve systems and other degenerated equations. This correspondence explains various degeneration phenomena of Painleve equations.

Furthermore, MPS include linear 2 systems which are equivalent to hypergeometric or confluent hypergeometric equations. This part is a joint work with N.M.J.Woodhouse.