Lattices of minimal covolume in SLn(R)
Abstract
The objective of this paper is to determine the lattices of minimal covolume in SLn(R), for n greater than 3. The answer turns out to be the simplest one: SLn(Z) is, up to automorphism, the unique lattice of minimal covolume in SLn(R). In particular, lattices of minimal covolume in SLn(R) are non-uniform when n is greater than 3, contrasting with Siegel's result for SL2(R). This answers for SLn(R) the question of Lubotzky: is a lattice of minimal covolume typically uniform or not?
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