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 u1 = (2, - 1, - 1)T / √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 the Majorana neutrino mass matrix, we find the almost unique solution ℤq x S4 where the cyclic factor ℤq with q = 1, 2, 3, ... is irrelevant for obtaining u1 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. [ABSTRACT FROM AUTHOR]