  We sharpen the orbit method for finite groups of small nilpotence class by
associating representations to functionals on the corresponding Lie rings. This
amounts to describing compatible intertwiners between representations
parameterized by an additional choice of polarization. Our construction is
motivated by the theory of the linearized Weil representation of the symplectic
group. In particular, we provide generalizations of the Maslov index and the
determinant functor to the context of finite abelian groups.
