Abstract
We prove a partial converse to the main theorem of the author’s previous paper Proper affine actions: a sufficient criterion (submitted; available at arXiv:1612.08942). More precisely, let G be a semisimple real Lie group with a representation $$\rho $$ on a finite-dimensional real vector space V, that does not satisfy the criterion from the previous paper. Assuming that $$\rho $$ is irreducible and under some additional assumptions on G and $$\rho $$, we then prove that there does not exist a group of affine transformations acting properly discontinuously on V whose linear part is Zariski-dense in $$\rho (G)$$.
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