Algebraic & Geometric Topology 7 (2007) 1099–1117

DOI: 10.2140/agt.2007.7.1099

arXiv: math.GR/0701493

Abstract

We give concrete constructions of discrete and faithful representations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we find a general criterion for when discrete and faithful representations exist, and show that the criterion is satisfied in particular cases. There are direct applications towards constructing representations of surface groups into higher-rank Lie groups, and, in particular, into lattices in higher-rank Lie groups.

Keywords

Artin groups, Lie groups

Mathematical Subject Classification

Primary: 20F36

Secondary: 53C35

References

Publication

Received: 2 February 2007
Revised: 8 June 2007
Accepted: 12 June 2007
Published: 2 August 2007

Authors