Hierarchy of B\"acklund Transformation Groups of the Painlev\'e Systems
Abstract
For each Painlev\'e system PJ except the first one, we have a B\"acklund transformation group which is a lift of an affine Weyl group. In this paper, we show that the B\"acklund 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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