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 \(\Gamma_0 < G\) which realises this minimum. This completes the work begun in Part I, which considered the cases when \(G\) admits an edge-transitive lattice.