The optical generation of high-order harmonics is known to have a strong polarization dependence: In contrast to linearly polarized excitation, circularly polarized light induces practically no harmonics. In the current paper we focus on atomic targets, the case when a well-established physical picture explains the effect: For circular polarization, the photoionized electrons never return to their parent nuclei, and the energy they gained while being accelerated by the field is not transferred into high-order harmonic radiation. This is essentially a picture that is based on real-space electron trajectories (or the dynamics of the wave functions). Here, we provide an alternative description that uses the discrete Sturmian basis, and points out how quantum mechanical interference effects and selection rules can explain the polarization dependence of the process. This emphasizes the importance of space-time symmetries during the process of high-order harmonic generation.