Symmetric powers and a problem of Kollar and Larsen

Details Symmetric powers and a problem of Kollar and Larsen Symmetric powers and a problem of Kollar and Larsen

2008-10-05

arxiv.org/abs/0810.0853v1

Mathematics

Representation Theory

49 pages. Inventiones Mathematicae, to appear

Scientific paper

10.1007/s00222-008-0140-z

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.

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