STABLE AND WELL-ROUNDED LATTICES IN DIAGONAL ORBITS

摘要

Let A subset of SLn(R) be the group of diagonal matrices with positive diagonal, let STn subset of X-n := SLn(R)/SLn(Z) be the set of stable lattices, and let WRn subset of X-n be the set of well-rounded lattices. We prove that any A-orbit in X-n intersects both STn and WRn.