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Abstract
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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.
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Keywords
Artin groups, Lie groups
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Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 53C35
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Publication
Received: 2 February 2007
Revised: 8 June 2007
Accepted: 12 June 2007
Published: 2 August 2007
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