Proper affine actions in non-swinging representations

Ilia Smilga

doi:10.4171/GGD/447

Proper affine actions in non-swinging representations

Group Theory 2018-10-01 v2 Representation Theory

Authors: Ilia Smilga

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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 $V$ .

Keywords

algebraic group actions representation theory of groups affine algebraic geometry

Cite

@article{arxiv.1605.03833,
  title  = {Proper affine actions in non-swinging representations},
  author = {Ilia Smilga},
  journal= {arXiv preprint arXiv:1605.03833},
  year   = {2018}
}

Comments

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

Proper affine actions in non-swinging representations

Abstract

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