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arXiv · 1705.09742

Lattices of minimal covolume in SL_n(R)

François Thilmany
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Abstract

The objective of this paper is to determine the lattices of minimal covolume in SL_n(R), for n greater than 3. The answer turns out to be the simplest one: SL_n(Z) is, up to automorphism, the unique lattice of minimal covolume in SL_n(R). In particular, lattices of minimal covolume in SL_n(R) are non-uniform when n is greater than 3, contrasting with Siegel's result for SL_2(R). This answers for SL_n(R) the question of Lubotzky: is a lattice of minimal covolume typically uniform or not?

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François Thilmany. 2017-05-26. Lattices of minimal covolume in SL_n(R). https://doi.org/10.1112/plms.12161

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