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Limits under conjugacy of the diagonal subgroup in $ SL_n(\mathbb{R})$


Author: Arielle Leitner
Journal: Proc. Amer. Math. Soc. 144 (2016), 3243-3254
MSC (2010): Primary 20-XX; Secondary 22-XX
DOI: https://doi.org/10.1090/proc/12959
Published electronically: December 22, 2015
MathSciNet review: 3503693
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Abstract: We give quadratic bounds on the dimension of the space of conjugacy classes of subgroups of $ SL_n(\mathbb{R})$ that are limits under conjugacy of the diagonal subgroup. We give the first explicit examples of abelian $ n-1$-dimensional subgroups of $ SL_n(\mathbb{R})$ which are not such a limit, and show that all such abelian groups are limits of the diagonal group iff $ n \leq 4$.


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Additional Information

Arielle Leitner
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Address at time of publication: Technion, Institute of Technology, Haifa, Israel 32000
Email: eleitner@tx.technion.ac.il

DOI: https://doi.org/10.1090/proc/12959
Keywords: Conjugacy limit, geometric transition
Received by editor(s): January 14, 2015
Received by editor(s) in revised form: June 11, 2015, June 30, 2015, and September 14, 2015
Published electronically: December 22, 2015
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society

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