On the monodromy of irreducible symplectic manifolds

Exploiting recent results on the ample cone of irreducible symplectic manifolds, we provide a different point of view for the computation of their monodromy groups. In particular, we give the final step in the computation of the monodromy group for generalised Kummer manifolds and we prove that the monodromy of O'Grady's ten dimensional manifold is smaller than what was expected.