Gauge Model for Maximal Neutrino Mixing

The recently announced Super-Kamiokande data on atmospheric neutrino oscillation seems to require a maximal mixing between the $\nu_{\mu}$ and $\nu_{\tau}$ within the conventional three neutrino picture. It is then tempting to suggest as has been done in literature, that the solar neutrino deficit be also understood as resulting from a maximal mixing between $\nu_e$ and $\nu_{\mu}$. In this letter, we propose a left-right symmetric extension of the standard model where permutation symmetry leads to one of the maximal mixing patterns in a technically natural manner. The double seesaw mechanism gives small Majorana masses for neutrinos needed to understand the atmospheric as well as the solar neutrino puzzles.