Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems

preprint2004arXivOpen access

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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