Some explicit cocycles on the Furstenberg boundary for products of isometries of hyperbolic spaces and $\mathrm{SL}(3,\mathbb{K})

Nicolas Monod showed that the evaluation map $H^*_m(G\curvearrowright G/P)\longrightarrow H^*_m(G)$ between the measurable cohomology of the action of a connected semisimple Lie group $G$ on its Furstenberg boundary $G/P$ and the measurable cohomology of $G$ is surjective with a kernel that can be entirely described in terms of invariants in the cohomology of the maximal split torus $A