Symmetric representation of the elements of the Conway group 0

• Autores: Robert T. Curtis, B. T. Fairbairn
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 8, 2009, págs. 1044-1067
• Idioma: inglés
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• Resumen

  • In this paper we represent each element of the Conway group 0 as a permutation on 24 letters from the Mathieu group M24, 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 , the sets of 24 mutually orthogonal 4-vectors in the Leech lattice ? often referred to as frames of reference or crosses, as they are fundamental to our procedure. In particular we describe the 19 orbits of M24 on these crosses.