, Volume 112, Issue 1, pp 225-237

Arithmeticity vs. Nonlinearity for Irreducible Lattices

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Abstract

We establish an arithmeticity vs. nonlinearity alternative for irreducible lattices in suitable product groups, for instance products of topologically simple groups. This applies notably to a (large class of) Kac–Moody groups. The alternative relies heavily on the superrigidity theorem we propose since we follow Margulis’ reduction of arithmeticity to superrigidity.

Mathematics Subject Classiffications (2000). 22E40, 22E50, 53C24, 20G15