String interactions and discrete symmetries of the pp-wave background

Free string theory on the plane-wave background displays a discrete Z2 symmetry exchanging the two transverse SO(4) rotation groups. This symmetry should be respected also at the interacting level. We show that the zero-mode structure proposed in Chu et al (2002 Preprint hepth/0208148) can be completed to a full kinematical vertex, contrary to claims appearing in the previous literature. We also comment on the relation with recent works on the string-bit formalism and on the comparison with the field theory side of the correspondence.