  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.
