2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127569We present an new system of ordinary differential equations with affine Weyl group symmetry of type E_6^{(1)}. This system is expressed as a Hamiltonian system of sixth order with a coupled Painleve VI Hamiltonian.14 pagesMathematical PhysicsRepresentation Theory34M55; 17B80; 37K10Coupled Painleve VI system with E_6^{(1)} symmetrytext