  We study the Lusztig-Vogan bijection for the case of a local system. We
compute the bijection explicitly in type A for a local system and then show
that the dominant weights obtained for different local systems on the same
orbit are related in a manner made precise in the paper. We also give a
conjecture (putatively valid for all groups) detailing how the weighted Dynkin
diagram for a nilpotent orbit in the dual Lie algebra should arise under the
bijection.
