  We study the time reversal and space inversion symmetry properties of those
transfer matrices mostly used in the calculation of energy spectra and
transport-process. We study the time reversal and space inversion symmetry
properties of those transfer matrices mostly used in the calculation of energy
spectra and transport-process quantities. We determine the unitary
transformation relating transfer matrices. We consider the Kohn-Luttinger model
for a quasi-2D system and show that even though the system studied in the (4 x
4) scheme satisfies all the symmetry requirements, the (2 x 2)subspaces do not
fulfill such constrains, except in the Gamma point of the Brillouin Zone. We
find new exchange properties between the (2\times 2)subspace quantities.
