  In this paper a monodromy invariant for isotropic classes on generalized
Kummer type manifolds is constructed. This invariant is used to determine the
polarization type of Lagrangian fibrations on such manifolds - a notion which
was introduced in an earlier paper of the author. The result shows that the
polarization type of a Lagrangian fibration of generalized Kummer type depends
on the connected component of the moduli space.
