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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57017A 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.13 pagesMathematical PhysicsRepresentation TheoryA new Lax pair for the sixth Painlevé equation associated with $\hat{\mathfrak{so}}(8)$text