  In the basis where the charged lepton mass matrix is diagonal, the
left-handed neutrino mass matrix is invariant under the permutation of the
second and third generations if, and only if, the reactor angle $\theta_{13}$
is zero and the atmospheric mixing angle $\theta_{23}$ is maximal. In the
presence of the seesaw mechanism, this symmetry leads to an inverted hierarchy,
with $m_3=0$. This inverted mass spectrum is doubly protected if the
right-handed neutrinos also have a 2-3 symmetry.
