The complex Lorentzian Leech lattice and the bimonster
Abstract
Description
We find 26 reflections in the automorphism group of the the Lorentzian Leech lattice L over Z[exp(2*pi*i/3)] that form the Coxeter diagram seen in the presentation of the bimonster. We prove that these 26 reflections generate the automorphism group of L. We find evidence that these reflections behave like the simple roots and the vector fixed by the diagram automorphisms behaves like the Weyl vector for the refletion group.
24 pages, 3 figures, revised and proof corrected. Some small results added. to appear in the Journal of Algebra
24 pages, 3 figures, revised and proof corrected. Some small results added. to appear in the Journal of Algebra