Lattices of minimal covolume in $SL_n(\mathbb{R})$
(2019) Proceedings of the London Mathematical Society — Vol. 118, n° 1, p. 78-102 (2019)
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- Abstract
- The objective of this paper is to determine the lattices of minimal covolume in $SL_n(\mathbb{R})$, for$ n \geq 3$. The answer turns out to be the simplest one: $SL_n<mathbb{(Z})$ is, up to automorphism, the unique lattice of minimal covolume in $SL_n(\mathbb{R})$. In particular, lattices of minimal covolume in $SL_n(\mathbb{R})$ are non-uniform when $n \geq 3$, contrasting with Siegel’s result for $SL_2(\mathbb{R})$. This answers for $SL_n(\mathbb{R})$ the question of Lubotzky: is a lattice of minimal covolume typically uniform or not?
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Thilmany, F. (2019). Lattices of minimal covolume in $SL_n(\mathbb{R})$. Proceedings of the London Mathematical Society, 118(1), 78-102. https://doi.org/10.1112/plms.12161 (Original work published 2019)