Neutrino mixing based on mass matrices with a 2 <-> 3 symmetry

Under an assumption that the 2 <-> 3 symmetry is broken only through phases, we give a systematic investigation of possible lepton mass matrix forms without referring to explicit parameter values. Two types of the 2 <-> 3 symmetry are investigated: one is that the left- and right-handed fields (f(L),f(R)) obey the symmetry, and another one is that only f(L) obeys the symmetry. In the latter case, in spite of no 2 <-> 3 symmetry in the Majorana mass matrix M-R for nu(R), the neutrino seesaw mass matrix still obeys the 2 <-> 3 symmetry. Possible phenomenology is discussed.