Barnes–Wall lattice

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In mathematics, the Barnes–Wall lattice Λ16, discovered by Eric Stephen Barnes and G. E. (Tim) Wall ((Barnes Wall)), is the 16-dimensional positive-definite even integral lattice of discriminant 28 with no norm-2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 2, and is analogous to the Coxeter–Todd lattice. The automorphism group of the Barnes–Wall lattice has order 89181388800 = 221 35 52 7 and has structure 21+8 PSO8+(F2).

The genus of the Barnes–Wall lattice was described by (Scharlau Venkov) and contains 24 lattices; all the elements other than the Barnes–Wall lattice have root system of maximal rank 16.

The Barnes–Wall lattice is described in detail in (Conway Sloane).

References

|mr=1282375 
|last=Scharlau 
|first=Rudolf 
|last2=Venkov 
|first2=Boris B. 
|title=The genus of the Barnes–Wall lattice. 
|journal=Comment. Math. Helv. 
|volume=69 
|year=1994 
|issue=2 
|pages=322–333 
|url=http://retro.seals.ch/digbib/view?did=c1:421661&sdid=c1:422358
|doi=10.1007/BF02564490 

|citeseerx=10.1.1.29.9284

External links