Journal
JOURNAL OF ALGEBRA
Volume 309, Issue 1, Pages 32-56Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jalgebra.2006.05.033
Keywords
complex Leech lattice; complex hyperbolic reflection group; monster; Weyl group; Coxeter diagram
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We find 26 reflections in the automorphism, group of the Lorentzian Leech lattice L over Z[e(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 reflection group. (c) 2006 Elsevier Inc. All rights reserved.
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