A geometric approach to tau-functions of difference Painlevé equations

Details A geometric approach to tau-functions of difference Painlevé equations A geometric approach to tau-functions of difference Painlevé equations

2008-04-10

arxiv.org/abs/0804.1680v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages

Scientific paper

10.1007/s11005-008-0251-x

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 Painlev\'e equations.

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