Construction of Milnorian representations

2018/02/20 by Smilga, Ilia
#20G05 #20G20 #20H15 #22E40 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1802.07193

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 ρ on a finite-dimensional real vector space V, that does not satisfy the criterion from the previous paper. Assuming that ρ is irreducible and under some additional assumptions on G and ρ, 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 ρ(G).

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