On the index system of well-rounded lattices

Abstract

Let \Lb be a lattice in an $n$-dimensional Euclidean space $E$ and let \Lb' be a Minkowskian sublattice of \Lb, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of \Lb. We consider the set of possible quotients \Lb/\Lb' which may exists in a given dimension or among not too large values of the index [\Lb:\Lb'], indeed [\Lb:\Lb']\le 4, or dimension $n\le 8$.Comment: 17 page