Irreducible representations of the symmetry groups of polymer molecules. III. Consequences of time-reversal symmetry

For pt.II see ibid., vol.14, no.4, p.777 (1981). Systematic degeneracies of electron and phonon energy spectra of stereoregular polymers are determined by the dimensions of unitary irreducible representations (reps) of line groups (L), as far as the spatial symmetries are concerned. However, time reversal ( theta ) invariance of the Hamiltonian can bring in some extra degeneracies. These are determined for the reps of all the line groups. A physical interpretation of the results is given in terms of the action of theta onto the quantum numbers arising from line-group symmetry. Finally, corepresentations of the groups L^A=L+ theta L and the corresponding symmetry-adapted bases are also obtained.