Geodesic
On semisimple representations of universal lattices
Daniel K. Shenfeld1
1Princeton University, USA
Groups, geometry, and dynamics, Tome 4 (2010) no. 1, pp. 179-193

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DOI

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.
DOI : 10.4171/ggd/79
Classification : 20-XX, 13-XX, 53-XX, 00-XX
Mots-clés : Universal lattices, superrigidity, arithmetic groups, arithmetic lattices

Daniel K. Shenfeld  1

1 Princeton University, USA 
Daniel K. Shenfeld. On semisimple representations of universal lattices. Groups, geometry, and dynamics, Tome 4 (2010) no. 1, pp. 179-193. doi: 10.4171/ggd/79
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