Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems

Masaki Suzuki, Nobuhiko Tahara, Kyoichi Takano

For each Painlevé system P_J except the first one, we have a Bäcklund transformation group which is a lift of an affine Weyl group. In this paper, we show that the Bäcklund transfo…