Certain Important Lattices and Their Properties

Abstract

This chapter describes the properties of a number of important lattices, including the cubic lattice Z ⁿ , the root lattices A _n , D _n , E ₆, E ₇, E ₈, the Coxeter-Todd lattice K ₁₂, the Barnes-Wall lattice Λ₁₆, the Leech lattice Λ₂₄, and their duals. Among other things we give their minimal vectors, densities, covering radii, glue vectors, automorphism groups, expressions for their theta series, and tables of the numbers of points in the first fifty shells. We also include a brief discussion of reflection groups and of the technique of gluing lattices together.