A new Lax pair for the sixth Painlevé equation associated with $\widehat{\mathfrak{so}}(8)$

Abstract

A new Lax pair for the sixth Painlevé equation $P_{VI}$ is constructed in the framework of the loop algebra $\mathfrak{so}(8)[z,z^{-1}]$. The whole affine Weyl group symmetry of $P_{VI}$ is interpreted as gauge transformations of the corresponding linear problem.

arXiv comment13 pages

References in corpus (1)

• Birational Weyl group action arising from a nilpotent Poisson algebra

Cited by in corpus (3)

• Quantum Baxter-Belavin R-matrices and multidimensional Lax pairs for Painleve VI
• Special polynomials related to the supersymmetric eight-vertex model: A summary
• Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains