  We prove a conjecture of Kollar and Larsen on Zariski closed subgroups of
$GL(V)$ which act irreducibly on some symmetric power $Sym^{k}(V)$ with $k \geq
4$. This conjecture has interesting implications, in particular on the holonomy
group of a stable vector bundle on a smooth projective variety, as shown by the
recent work of Balaji and Kollar.
