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## Construction of Milnorian representations

math. arxive. Cornell University, 2018. No. 1802.07193.
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).