Representations of Surface Groups and Right-Angled Artin Groups in Higher Rank

Details Representations of Surface Groups and Right-Angled Artin Groups in Higher Rank Representations of Surface Groups and Right-Angled Artin Groups in Higher Rank

2007-01-17

arxiv.org/abs/math/0701493v2

Mathematics

Group Theory

17 pages, 2 figures

Scientific paper

We give very flexible, concrete constructions of discrete and faithful epresentations 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.

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