Commensurators of some non-uniform tree lattices and Moufang twin trees

Abstract

Sh. Mozes showed that the commensurator of the lattice ${\mathrm{PSL}}_2({\mathbf{F}}_p[t{}^{-1}])$ is dense in the full automorphism group of the Bruhat-Tits tree of valency $p+1$, the latter group being much bigger than ${\mathrm{PSL}}_2({\mathbf{F}}_p((t)))$. By G.A. Margulis' criterion, this density is a generalized arithmeticity result. We show that the density of the commensurator holds for many tree-lattices among those called of Nagao type by H. Bass and A. Lubotzky. The result covers many lattices obtained via Moufang twin trees.

23 pages, 3 figures

References in corpus (1)

• Topological groups of Kac-Moody type, Fuchsian twinnings and their lattices