I will present some recent results on the automorphism group of irreducible holomorphic symplectic manifolds polarised by an ample divisor of square two with respect to the Beauville-Bogomolov-Fujiki quadratic form. These results concern the deformation class of the Hilbert scheme of two points on a generic projective K3 surface. This is a collaboration with Andrea Cattaneo and Alessandra Sarti.