Limits under conjugacy of the diagonal subgroup in 𝑆𝐿_{𝑛}(ℝ)

Leitner, Arielle

doi:10.1090/proc/12959

Limits under conjugacy of the diagonal subgroup in $SL_n(\mathbb {R})$
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Proc. Amer. Math. Soc. 144 (2016), 3243-3254 Request permission

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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