We present a recently developed ab initio method based on many-body perturbation theory to calculate the optical absorption spectrum of one-dimensional systems with helical symmetry. Our scheme involves a local, symmetrized basis set which allows for the calculation of large systems otherwise prohibitive in the standard plane-wave approach. It also affords an understanding of the symmetry character of the single-particle states and the excitonic wave functions, which has the advantage of determining in a precise way the selection rules related to the optical transitions of the system in question. We apply our method to single-wall carbon nanotubes of type (4,2) and present the calculated self-energy corrections, absorption spectra, and excitonic states; we find that GW corrections are substantial and excitonic effects strongly affect the optical properties.