Lattices of minimal covolume in SL_n(R)
arXiv:1705.09742 · doi:10.1112/plms.12161
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?
28 pages, 1 figure, 6 tables