Symmetric powers and a problem of Kollar and Larsen

Abstract

We prove a conjecture of Kollar and Larsen on Zariski closed subgroups of $GL(V)$ which act irreducibly on some symmetric power $Sy{m}^k(V)$ with $k\ge 4$. 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.

49 pages. Inventiones Mathematicae, to appear