  Let $K$ be a number field, $\OK$ be its ring of integers. We introduce the
notion of compactified representation of $GL_N(\OK)$ and, we see how to
associate to a hermitian vector bundle $\E$ over $\Spec(\OK)$ and a
compactified representation $\T$, a hermitian tensor bundle $\E_T$. We can
prove then that there exists a lower bound for the heights of points
$x\in\P(\E_T)$ with $SL_N(K)$--semistable generic fibre in terms of the degree
of $\E$ and some universal constants depending only on the compactified
representation. We give then three applications: a universal lower bound for
general flag varieties, an application to the adjoint representation of
$SL_N(K)$ and a construction of a height on the moduli space of semistable
vector bundles over algebraic curves.
