Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems
Masaki Suzuki, Nobuhiko Tahara, Kyoichi Takano
Abstract
For each Painlevé system PJ 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 transformation groups for J=V,IV,III,II are successively obtained from that for J=VI by the well known degeneration or confluence processes.
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