New Partial Symmetries from Group Algebras for Lepton Mixing

Recent stringent experiment data of neutrino oscillations induces partial symmetries such as Z2 and Z2 × CP to derive lepton
mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern
could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could
express a residual CP symmetry. Lepton mixing matrices from S3 group algebras are of the trimaximal form with the μ − τ
reflection symmetry. Accordingly, elements of S3 group algebras are equivalent to Z2 × CP. Comments on S4 group algebras are
given. The predictions of Z2 × CP broken from the group S4 with the generalized CP symmetry are also obtained from elements
of S4 group algebras.