Abstract
A conjugacy limit group is the limit of a sequence of conjugates of the positive diagonal Cartan subgroup, \(C \le SL _3(\mathbb {R}).\) We prove a variant of a theorem of Haettel, and show that up to conjugacy, C has five possible conjugacy limit groups. Each conjugacy limit group is determined by a nonstandard triangle. We give a criterion for a sequence of conjugates of C to converge to each of the five conjugacy limit groups.
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Acknowledgments
The author thanks Daryl Cooper for many insightful conversations, patience, and for suggesting the use of the hyperreals. The author thanks Darren Long, David Dumas, and Jeff Danciger for many helpful discussions. The referee also provided some excellent ideas for restructuring the paper, and improving the clarity of some of the arguments. The author was partially supported by NSF Grants DMS–0706887, 1207068 and 1045292. The author spent fall 2013 at ICERM, and had many illuminating discussions with the other visiting academics there. The author acknowledges support from U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 RNMS: GEometric structures And Representation varieties (the GEAR Network).
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Leitner, A. Conjugacy limits of the diagonal cartan subgroup in \({\varvec{SL}}_\mathbf{3 }({\varvec{\mathbb {R}}})\) . Geom Dedicata 180, 135–149 (2016). https://doi.org/10.1007/s10711-015-0095-3
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DOI: https://doi.org/10.1007/s10711-015-0095-3