Induced automorphisms on irreducible symplectic manifolds

We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of K3^[n]-type is, in fact, induced by an automorphism of a K3 surface, and the manifold is a moduli space of stable objects on the K3. This criterion is applied to the classification of non-symplectic prime order automorphisms on manifolds of K3^[2]-type, and we prove that almost all cases are covered. Variations of this notion and the above criterion are introduced and discussed for the other known deformation types of irreducible symplectic manifolds. Furthermore, we provide a description of the picard lattice of several irreducible symplectic manifolds having a lagrangian fibration.