On symplectic automorphisms of hyperk\"ahler fourfolds of K3^[2] type

The present paper proves that finite symplectic groups of automorphisms of hyperk"ahler fourfolds deformation equivalent to the Hilbert scheme of two points on a $K3$ surface are contained in the simple group $C{o}_1$. Then we give an example of a symplectic automorphism of order 11 on the Fano scheme of lines of a cubic fourfold.