U-Duality and the Leech Lattice
Abstract
It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F4 in E6(-26), the U-duality group for N=2, D=5 exceptional magic supergravity. By mapping points of the Leech lattice to black hole charge vectors, it is seen Co0 is generated by U-duality transformations acting as rotations in the charge space for BPS black holes.
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