Profinite Completions and Representations of Finitely Generated Groups
Abstract
In previous work, the author and his collaborators developed a relationship in the SL(2, C) representation theories of two finitely generated groups with isomorphic profinite completions assuming a certain strong representation rigidity for one of the groups. This was then exploited as one part of producing examples of lattices in SL(2, C) which are profinitely rigid. In this article, the relationship is extended to representations in any connected reductive algebraic groups under a weaker representation rigidity hypothesis. The results are applied to lattices in higher rank Lie groups where we show that for some such groups, including SL(n, Z) for n ≥ 3, they are either profinitely rigid, or they contain a proper Grothendieck subgroup.
Degree
Ph.D.
Advisors
McReynolds, Purdue University.
Subject Area
Mathematics
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