  Recent optical absorption/emission experiments showed that the lower energy
optical transitions in carbon nanotubes are excitonic in nature, as predicted
by theory. These experiments were based on the symmetry aspects of free
electron-hole states and bound excitonic states. The present work shows,
however, that group theory does not predict the selection rules needed to
explain the two photon experiments. We obtain the symmetries and selection
rules for the optical transitions of excitons in single-wall carbon nanotubes
within the approach of the group of the wavevector, thus providing important
information for the interpretation of theoretical and experimental optical
spectra of these materials.
