A new class of invariants in the lepton sector

We construct a new set of combinations from the mass matrices of the charged leptons and neutrinos that are invariant under basis transformation, hereafter {\it the} invariants. We use these invariants to study various symmetries and neutrino mass textures in a basis independent way. In particular, we show that by using these invariants the ansatz such as $\mu-\tau$ exchange and reflection symmetries, various texture zeros and flavor symmetries can be expressed in a general basis.