From KP/UC hierarchies to Painleve equations
Teruhisa Tsuda (Kyushu University, Japan)
Tuesday 16th June, 2009 15:00-16:00 Mathematics Building, room 204
The universal character (K.Koike 1989 Adv. Math.) is a polynomial attached to a pair of partitions and is a generalization of the Schur polynomial. As discovered by M.Sato the Schur polynomial characterizes the KP hierarchy, which is probably the most important infinite-dimensional integrable system. On the other hand an extension of the KP hierarchy, called the UC hierarchy, was introduced as a counterpart associated with the universal character (T 2004 CMP). In this talk we begin by a brief review of KP/UC hierarchies, and then show how they are related to the Painleve equations through similarity reductions.