Cusps of lattices in rank 1 Lie groups over local fields
Abstract
Description
Let G be the group of rational points of a semisimple algebraic group of rank 1 over a nonarchimedean local field. We improve upon Lubotzky's analysis of graphs of groups describing the action of lattices in G on its Bruhat-Tits tree assuming a condition on unipotents in G. The condition holds for all but a few types of rank 1 groups. A fairly straightforward simplification of Lubotzky's definition of a cusp of a lattice is the key step to our results. We take the opportunity to reprove Lubotzky's part in the analysis from this foundation.
to appear in Geometriae Dedicata
to appear in Geometriae Dedicata