Proper affine actions in non-swinging representations

Abstract

For a semisimple real Lie group $G$ with an irreducible representation $\rho$ on a finite-dimensional real vector space $V$, we give a sufficient criterion on $\rho$ for existence of a group of affine transformations of $V$ whose linear part is Zariski-dense in $\rho (G)$ and that is free, nonabelian and acts properly discontinuously on $V$.