Cocompact lattices of minimal covolume in rank 2 Kac-Moody groups, Part II

Inna (Korchagina) Capdeboscq and Anne Thomas

Abstract

Let $G$ be a topological Kac-Moody group of rank 2 with symmetric Cartan matrix, defined over a finite field $F_q$. An example is $G=\mathrm{SL}(2,F_q((t^{-1})))$. We determine a positive lower bound on the covolumes of cocompact lattices in $G$, and construct a cocompact lattice ${\mathrm{\Gamma }}_0<G$ which realises this minimum. This completes the work begun in Part I, which considered the cases when $G$ admits an edge-transitive lattice.