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arXiv · 1612.08765

Intersections of diagonal orbits

Omri N. Solan
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Abstract

Let $A\subseteq SL_n(\mathbb{R})$ group of diagonal matrices with positive diagonal, let ${\rm ST}_n\subseteq X_n:=SL_n(\mathbb{R})/SL_n(\mathbb{Z})$ be the set of stable lattices, and let ${\rm WR}_n\subseteq X_n$ be the set of well-rounded lattices. We prove that any $A$-orbit in $X_n$ intersects both ${\rm ST}_n$ and ${\rm WR}_n$.

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Omri N. Solan. 2016-12-27. Intersections of diagonal orbits. https://arxiv.org/abs/1612.08765

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