Hierarchy of B\"acklund Transformation Groups of the Painlev\'e Systems
  For each Painlev\'e system P_J 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. 
Masaki Suzuki, Nobuhiko Tahara and Kyoichi Takano