A geometric approach to tau-functions of difference Painlevé equations

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.

12 pages

References in corpus (2)

• Quivers and difference Painleve equations
• Universal character and q-difference Painlevé equations with affine Weyl groups

Cited by in corpus (3)

• Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E^{(1)}_n
• On the lattice-geometry and birational group of the six-point multi-ratio equation
• Reduction of quad-equations consistent around a cuboctahedron I: additive case