TY - JOUR
T1 - Symmetric representation of the elements of the Conway group
AU - Curtis, Robert
AU - Fairbairn, BT
PY - 2009/3/6
Y1 - 2009/3/6
N2 - In this paper we represent each element of the Conway group .0 as a permutation on 24 letters from the Mathieu group M-24, followed by a codeword of the binary Golay code (which corresponds to a diagonal matrix taking the value -1 on the positions of the codeword and 1 otherwise), followed by a word of length at most 4 in a highly symmetric generating set. We describe an algorithm for multiplying elements represented in this way, that we have implemented in MAGMA. We include a detailed description Of (Lambda) over bar (4), the sets of 24 mutually orthogonal 4-vectors in the Leech lattice Lambda often referred to as frames of reference or crosses, as they are fundamental to our procedure. In particular we describe the 19 orbits Of M-24 on these crosses. (C) 2009 Elsevier Ltd. All rights reserved.
AB - In this paper we represent each element of the Conway group .0 as a permutation on 24 letters from the Mathieu group M-24, followed by a codeword of the binary Golay code (which corresponds to a diagonal matrix taking the value -1 on the positions of the codeword and 1 otherwise), followed by a word of length at most 4 in a highly symmetric generating set. We describe an algorithm for multiplying elements represented in this way, that we have implemented in MAGMA. We include a detailed description Of (Lambda) over bar (4), the sets of 24 mutually orthogonal 4-vectors in the Leech lattice Lambda often referred to as frames of reference or crosses, as they are fundamental to our procedure. In particular we describe the 19 orbits Of M-24 on these crosses. (C) 2009 Elsevier Ltd. All rights reserved.
KW - Conway group
KW - Symmetric generation
KW - Leech lattice
U2 - 10.1016/j.jsc.2009.02.002
DO - 10.1016/j.jsc.2009.02.002
M3 - Article
SN - 1095-855X
JO - Journal of Symbolic Computation
JF - Journal of Symbolic Computation
ER -