Abstract
We present a unified description of birational representation of Weyl groups associated with T-shaped Dynkin diagrams, by using a particular configuration of points in the projective plane. A geometric formulation of tau-functions is given in terms of defining polynomials of certain curves. If the Dynkin diagram is of affine type (\({E_6^{(1)}}\) , \({E_7^{(1)}}\) or \({E_8^{(1)}}\)), our representation gives rise to the difference Painlevé equations.
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