A new class of invariants in the lepton sector

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We construct a new set of combinations from the mass matrices of the charged leptons and neutrinos that are invariant under basis transformation, hereafter 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 μ-τ exchange and reflection symmetries, various texture zeros and flavor symmetries can be expressed in a general basis.