A4 and CP symmetry and a model with maximal CP violation

We study a second CP symmetry compatible with the A4 flavor group, which interchanges the representations 1′ and 1″. We analyze the lepton mixing patterns arising from the A4 and CP symmetry broken to residual subgroups Z3 and Z2×CP in the charged lepton and neutrino sectors respectively. One phenomenologically viable mixing pattern is found, and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP phase, trivial Majorana phases and the correlation sin2⁡θ12cos2⁡θ13=1/3. We construct a concrete model based on the A4 and CP symmetry, the above interesting mixing pattern is achieved, the observed charged lepton mass hierarchy is reproduced, and the reactor mixing angle θ13 is of the correct order.