This note describes a unified approach to several superrigidity results, old and new, concerning representations of lattices into simple algebraic groups over local fields. For an arbitrary group L and a boundary B we associate certain generalized Weyl group W and show that any representation with a Zariski dense unbounded image in a simple algebraic group, L->H, defines a special homomorphism W->Weyl(H). This general fact allows to deduce the aforementioned superrigidity results.