Representations of surface groups and right-angled Artin groups in higher rank

Wang, Stephen

doi:10.2140/agt.2007.7.1099

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Representations of surface groups and right-angled Artin groups in higher rank

Stephen Wang

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 2000

Primary: 20F36

Secondary: 53C35

References

Publication

Received: 2 February 2007

Revised: 8 June 2007

Accepted: 12 June 2007

Published: 2 August 2007

Authors

Stephen Wang
Department of Mathematics Haverford College Haverford PA 19104 USA
http://www.haverford.edu/math/swang/

Volume 7, issue 2 (2007)