No cohomologically trivial non-trivial automorphism of generalized Kummer manifolds

Abstract: We prove that the natural representaion, on the total Betti cohomolgy group, of the automorphism group of a hyperk\"ahler manifold deformation equivalent to a generalized Kummer manifold is faithful. This is a sort of generalization of an earlier work of Beauville and a recent work of Boiss\'ere, Nieper-Wisskirchan and Sarti, concerning the representation on the second cohomology group.