On matrix Painlev\'e equations
Seminar Room 1, Newton Institute
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.