Leech Lattice - History

History

Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than the Leech lattice. O'Connor & Pall (1944) discovered a related odd unimodular lattice in 24 dimensions, now called the odd Leech lattice, whose even sublattice has index 2 in the Leech lattice. The Leech lattice was discovered in 1965 by John Leech (1967, 2.31, p. 262), by improving some earlier sphere packings he found (Leech 1964).

Conway (1968) calculated the order of the automorphism group of the Leech lattice, and discovered three new sporadic groups as a by-product: the Conway groups, Co₁, Co₂, Co₃.

Bei dem Versuch, eine Form aus einer solchen Klasse wirklich anzugeben, fand ich mehr als 10 verschiedene Klassen in Γ₂₄

Witt (1941, p.324), has a single rather cryptic sentence mentioning that he found more than 10 even unimodular lattices in 24 dimensions without giving further details. In a seminar in 1970 Ernst Witt claimed that one of the lattices he found in 1940 was the Leech lattice. See his collected works (Witt 1998, p. 328–329) for more comments and for some notes Witt wrote about this in 1972.