  We study the collective excitations and inelastic light scattering
cross-section of an electron gas confined in a GaAs/AlGaAs coaxial quantum
well. These system can be engineered in a core-multi-shell nanowire and inherit
the hexagonal symmetry of the underlying nanowire substrate. As a result, the
electron gas forms both quasi 1D channels and quasi 2D channels at the quantum
well bents and facets, respectively. Calculations are performed within the RPA
and TDDFT approaches. We derive symmetry arguments which allow to enumerate and
classify charge and spin excitations and determine whether excitations may
survive to Landau damping. We also derive inelastic light scattering selection
rules for different scattering geometries. Computational issues stemming from
the need to use a symmetry compliant grid are also investigated systematically.
