The symplectic structure of the SL_n(R)-Hitchin component

The SL_n(R)-Hitchin component of a closed surface is a special component in the character variety consisting of homomorphisms from the fundamental group of the surface to the Lie group SL_n(R). It carries a symplectic structure, defined by the Atiyah-Bott-Goldman form. I will provide an explicit computation of this symplectic form in terms of the generalized Fock-Goncharov coordinates of the Hitchin component (associated to a geodesic lamination on the surface).