  In part I of [1] we have developed the tensor and spin representation of
SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane
model. We attach to each face of a triangle the spherical function constructed
from the Dolginov-Biedenharn function.
  In part II we apply the same technique to the Lorentz invariant state sum
model. We need three new ingredients: the classification of the edges and the
corresponding subspaces that arises in the simplicial decomposition, the irreps
of SL(2,C) and its isomorphism to the bivectors appearing in the 4-simplices,
the need of a zonal spherical function from the intertwining condition of the
tensor product for the simple representations attached to the faces of the
simplicial decomposition.
