Discrete symmetries, roots of unity, and lepton mixing

We investigate the possibility that the first column of the lepton mixing matrix U is given by u(1) = (2,-1,-1)(T)/root 6. In a purely group-theoretical approach, based on residual symmetries in the charged-lepton and neutrino sectors and on a theorem on vanishing sums of roots of unity, we discuss the finite groups which can enforce this. Assuming that there is only one residual symmetry in theMajorana neutrino mass matrix, we find the almost unique solution Z(q) x S-4 where the cyclic factor Z(q) with q = 1, 2, 3,... is irrelevant for obtaining u(1) in U. Our discussion also provides a natural mechanism for achieving this goal. Finally, barring vacuum alignment, we realize this mechanism in a class of renormalizable models.