M. Moskowitz, R. D. Mosak:
Stabilizers of lattices in Lie groups
Journal of Lie Theory, vol. 4 (1), p. 1-16
Let $G$ be a connected Lie group with Lie algebra $\fg$, containing a
lattice $\Gamma$. We shall write $\Aut(G)$ for the group of all smooth
automorphisms of $G$. If $A$ is a closed subgroup of $\Aut(G)$ we denote
by $\Stab_A(\Gamma)$ the stabilizer of $\Gamma$ in $A$; for example, if
$G$ is $\R^n$, $\Gamma$ is $\Z^n$, and $A$ is $\SL(n,\R)$, then
$\Stab_A(\Gamma) = \SL(n,\Z)$. The latter is, of course, a lattice in
$\SL(n,\R)$; in this paper we shall investigate, more generally, when
$\Stab_A(\Gamma)$ is a lattice (or a uniform lattice) in $A$.