Full Escape of Mass for the Diagonal Group

Abstract

Building on the work of Cassels we prove the existence of infinite families of compact orbits of the diagonal group in the space of lattices which accumulate only on the divergent orbit of the standard lattice. As a consequence, we prove the existence of full escape of mass for sequences of such orbits, sharpening known results about possible partial escape of mass. The topological complexity of the visits of these orbits to a given compact set in the space of lattices is analyzed. Along the way we develop new tools to compute regulators of orders in a number fields.