Certain Important Lattices and Their Properties

  • J. H. Conway
  • N. J. A. Sloane
Chapter
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 290)

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.

Keywords

Root Lattice Automorphism Group Generator Matrix Weyl Group Minimal Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • J. H. Conway
  • N. J. A. Sloane

There are no affiliations available

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