Limits under conjugacy of the diagonal subgroup in $SL_n(\mathbb {R})$
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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 $n \leq 4$.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3503693