Quivers and difference Painleve equations

Abstract

We will describe natural `Lax pairs' for the difference Painleve equations with affine Weyl symmetry groups of types E6, E7 and E8, showing that they do indeed arise as symmetries of certain Fuchsian systems of differential equations.

30 pages, 14 figures. Dedicated to John McKay

References in corpus (5)

• Dual Isomonodromic Deformations and Moment Maps to Loop Algebras
• Quiver algebras, weighted projective lines, and the Deligne-Simpson problem
• Regge and Okamoto symmetries
• Painlevé equations and the middle convolution
• Katz's middle convolution algorithm

Cited by in corpus (13)

• Mirrors of 3d Sicilian theories
• Irregular connections and Kac-Moody root systems
• More Three Dimensional Mirror Pairs
• Global Weyl groups and a new theory of multiplicative quiver varieties
• Folding Orthosymplectic Quivers
• Hyperkahler manifolds and nonabelian Hodge theory of (irregular) curves
• A Lax Formalism for the Elliptic Difference Painlevé Equation
• Hyperpolygons and Hitchin systems
• Discrete Schlesinger Transformations, their Hamiltonian Formulation, and Difference Painlevé Equations
• Diagrams for nonabelian Hodge spaces on the affine line
• Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations
• On Some Applications of Sakai's Geometric Theory of Discrete Painlevé Equations
• A geometric approach to tau-functions of difference Painlevé equations