Abstract
This chapter describes the properties of a number of important lattices, including the cubic lattice Zn, the 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.
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Bibliography
Adol] J.-P. Adoul, La quantification vectorielle des signaux: approche algebrique,Ann. Te’écommun. 41 (1986), 158–177 [2, 20].
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Conway, J.H., Sloane, N.J.A. (1999). Certain Important Lattices and Their Properties. In: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften, vol 290. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6568-7_4
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DOI: https://doi.org/10.1007/978-1-4757-6568-7_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3134-4
Online ISBN: 978-1-4757-6568-7
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