  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 $\Gamma$ and a $\Gamma$-boundary $B$
we associate certain generalized Weyl group $W_{\Gamma,B}$ and show that any
representation with a Zariski dense unbounded image in a simple algebraic
group, $\rho:\Gamma\to \mathbf{H}$, defines a special homomorphism
$W_{\Gamma,B}\to {\rm Weyl}(\mathbf{H})$. This general fact allows to deduce
the aforementioned superrigidity results.
