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 $V$.

This paper generalizes the author's earlier paper arXiv:1406.5906 . The structure of the proof is similar; a few passages, especially sections 7 to 10, draw heavily on the previous paper. This is an updated version that takes into account reviewers' corrections

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