and the unitary matrix In order to simplify Eq. (11), we can rotate the matter fields leaving the bulk lagrangian L invariant. However, the localized terms become diagonal in flavor space (the terms proportional to x$_{l}$ and y$_{b,s}$ are actually flavor independent), except for the Majorana masses Dirichlet boundary conditions are modified in the presence of these boundary terms. Thus, on the UV brane and on the IR one From these equations we observe that the lepton doublet zero mode is shared by all mul- tiplets due to the non-zero values of x$_{l}$ , y$_{b}$ and y α $_{b}$, whereas y$_{s}$ splits the RH neutrino zero 8 Ω ≡ 1 √$_{3}$    1 1 1 1 ω ω 2 1 ω 2 ω    , ω = e 2 πi/ $^{3}$. (13) ζ$_{k}$ → Ω ζ$_{k}$, ∀ k, (14) − L UV = 1 2 ν ′ c 2 $_{R}$ˆ θ$_{M}$ ν ′ 2 R + x$_{l}$ ¯ l$_{1}$$_{L}$l$_{3}$$_{R}$ + h . c . + . . . , −L IR = ( R R ′ ) 4 [ √$_{3}$ v ′ Λ ′ ( y α b l$_{3}$$_{αL}$l$_{αR}$ + y α b ˜ l$_{3}$$_{αL}$ ˜ l$_{αR}$ + y α s e ′ 3 $_{αL}$e ′ αR ) + y$_{b}$ v ′ η Λ ′ l$_{1}$$_{L}$l$_{2}$$_{R}$ + ˜ l$_{1}$$_{L}$ ˜ l$_{2}$$_{R}$ ) + y$_{s}$ v ′ η Λ ′ ν ′ 1 $_{L}$ν ′ 2 R ] + h . c . + . . . , (15) ˆ θ$_{M}$ ≡ Ω θ$_{M}$ Ω =    ϵ$_{s}$ + 2 ϵ$_{t}$ 3 − ϵ$_{t}$ 3 − ϵ$_{t}$ 3 − ϵ$_{t}$ 3 2 ϵ$_{t}$ 3 ϵ$_{s}$ − ϵ$_{t}$ 3 − ϵ$_{t}$ 3 ϵ$_{s}$ − ϵ$_{t}$ 3 2 ϵ$_{t}$ 3    . (16) l$_{1}$$_{R}$ − x$_{l}$l$_{3}$$_{R}$ = 0 , l$_{3}$$_{L}$ + x ∗ l l$_{1}$$_{L}$ = 0 , ν ′ 2 L + ˆ θ † $_{M}$ν ′ c 2 R = 0 , (17) l$_{3}$$_{αR}$ $_{+}$√$_{3}$ v ′ Λ ′ y α b l$_{αR}$ = 0 , ˜ l$_{3}$$_{αR}$ $_{+}$√$_{3}$ v ′ Λ ′ y α $_{b}$˜ l$_{αR}$ = 0 , e ′ 3 αR $_{+}$√$_{3}$ v ′ Λ ′ y α s e ′ αR = 0 , l$_{αL}$ − √$_{3}$ v ′ Λ ′ y $^{α}$∗ b l$_{3}$$_{αL}$ = 0 , ˜ l$_{αL}$ − √$_{3}$ v Λ ′ y $^{α}$∗ b ˜ l$_{3}$$_{αL}$ = 0 , e ′ αL − √$_{3}$ v ′ Λ ′ y $^{α}$∗ s e ′ 3 αL = 0 , l$_{1}$$_{R}$ + y$_{b}$ v ′ η Λ ′ l$_{2}$$_{R}$ = 0 , ˜ l$_{1}$$_{R}$ + y$_{b}$ v ′ η Λ ′ ˜ l$_{2}$$_{R}$ = 0 , ν ′ 1 R + y$_{s}$ v η Λ ′ ν ′ 2 R = 0 , l$_{2}$$_{L}$ − y ∗ b v η Λ ′ l$_{1}$$_{L}$ = 0 , ˜ l$_{2}$$_{L}$ − y ∗ b v η Λ ′ ˜ l$_{1}$$_{L}$ = 0 , ν ′ 2 L − y ∗ s v η Λ ′ ν ′ 1 L = 0 . (18)