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Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems

Masaki Suzuki·Nobuhiko Tahara·Kyoichi Takano
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Abstract

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 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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Masaki Suzuki, Nobuhiko Tahara, Kyoichi Takano. 2004-05-28. Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems. https://doi.org/10.2969/jmsj%2F1190905457

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