Abstract
Let A ⊆ SLn(ℝ) be the group of diagonal matrices with positive diagonal, let STn ⊆ Xn := SLn(ℝ) / SLn(ℤ) be the set of stable lattices, and let WRn ⊆ Xn be the set of well-rounded lattices. We prove that any A-orbit in Xn intersects both STn and WRn.
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Acknowledgments
The author wishes to thank Barak Weiss for presenting the problem, his guidance, and his comments on earlier versions of the paper. The author also thanks Shachar Carmeli, Roman Karasev, and Lev Radzivilovsky for helpful discussions. The research was partially supported by the ERC starter grant DLGAPS 279893.
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Solan, O.N. Stable and well-rounded lattices in diagonal orbits. Isr. J. Math. 234, 501–519 (2019). https://doi.org/10.1007/s11856-019-1912-4
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DOI: https://doi.org/10.1007/s11856-019-1912-4