Groups, Geometry, and Dynamics

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Volume 4, Issue 1, 2010, pp. 179–193
DOI: 10.4171/GGD/79

Published online: 2009-12-23

On semisimple representations of universal lattices

Daniel K. Shenfeld[1]

(1) Princeton University, USA

We study finite-dimensional semisimple complex representations of the universal lattices Γn,k = SLn(ℤ[x1, …, xk]) (n ≥ 3). One may obtain such a representation by specializing x1, …, xk to some complex values and composing the induced homomorphism Γn,k → SLn(ℂ) with a rational representation of SLn(ℂ). We show that any semisimple representation coincides, on a subgroup of finite index, with a direct sum of tensor products of representations obtained in this way.

Keywords: Universal lattices, superrigidity, arithmetic groups, arithmetic lattices

Shenfeld Daniel: On semisimple representations of universal lattices. Groups Geom. Dyn. 4 (2010), 179-193. doi: 10.4171/GGD/79