✦ LIBER ✦
Construction of a 45,694-dimensional simple module of Lyons' sporadic group over GF(2)
✍ Scribed by Holger W Gollan; Gerhard O Michler
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 564 KB
- Volume
- 256
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
It is shown that the 2-modular reduction ~0 of the smallest nontrivial, rational, absolutely irreducible character X of Lyons' sporadic simple group Ly is irreducible. Furthermore, an explicit 45,694-dimensional irreducible matrix representation of Ly over the field GF(2) with two elements is given. The construction has been performed on a parallel computer of type IBM SP1 with i0 nodes. It uses the recent presentation of Ly as a permutation group on 9,606,125 points given by Cooperman, Finkelstein, Tselman, and York.