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arxiv math/0701493 v2 pith:S226YS5X submitted 2007-01-17 math.GR math.DGmath.GT

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

classification math.GR math.DGmath.GT
keywords groupshigher-rankrepresentationsartincriteriondiscretefaithfulparticular
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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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