Minimal Vectors of Pairs of Dual Lattices

AbstractWe classify n-dimensional pairs of dual lattices by their minimal vectors. This leads to the notion of a "perfect pair", a natural enlargement by duality of the usual notion of a perfect lattice, and we show that there are only finitely many of them in any given dimension. As an application, we obtain a finiteness theorem for pairs of dual lattices which are extremal with respect to the geometrical mean γ′ of their Hermite invariants