Donagi-Markman cubic for the generalised Hitchin system

Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We prove that the Balduzzi--Pantev formula holds along maximal rank symplectic leaves of the G-generalised Hitchin system.