  A very important open question related to the pygmy dipole resonance is about
its quite elusive collective nature. In this paper, within a harmonic
oscillator shell model, generalizing an approach introduced by Brink, we first
identify the dipole normal modes in neutron rich nuclei and derive the energy
weighted sum rule exhausted by the pygmy dipole resonance. Then solving
numerically the self-consistent Landau-Vlasov kinetic equations for neutrons
and protons with specific initial conditions, we explore the structure of the
different dipole vibrations in the $^{132}Sn$ system and investigate their
dependence on the symmetry energy. We evidence the existence of a distinctive
collective isoscalar-like mode with an energy well below the Giant Dipole
Resonance (GDR), very weakly dependent on the isovector part of the nuclear
effective interaction. At variance the corresponding strength is rather
sensitive to the behavior of the symmetry energy below saturation, which rules
the number of excess neutrons in the nuclear surface.
