Restrictions of characters and Weil characters in symplectic and unitary groups

We consider the representation theory of finite symplectic and unitary groups and examine restrictions of unipotent characters to maximal parabolic subgroups stabilizing an isotropic line with the goal of finding an upper bound for the multiplicities of these restrictions which does not depend on the field over which the group is defined. We work towards a reduction to the case of unipotent cuspidal characters