Irreducible representations of the symmetry groups of polymer molecules. I

Abstract

The line groups are the symmetry groups of stereoregular polymer molecules. For quantum mechanical applications one needs their unitary irreducible representations (reps). All the reps of the line groups whose isogonal point groups are C_n, C_nv, C_nh, S_2n, and D_n are constructed. For some line groups the reps are obtained as products of the reps of the translational subgroup and the reps of the isogonal point group. The rest of the reps are induced from those of the corresponding invariant subgroups of index two.