Moonshine paths for 3A and 6A nodes of the extended E8-diagram

JOURNAL OF ALGEBRA

卷:379

Article

Griess, Robert L., Jr.¹  Lam, Ching Hung² 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Acad Sinica, Inst Math, Taipei 10617, Taiwan

关键词: Monster group;    Moonshine;    Integral lattices;    Leech lattice;    Weyl group;    Involutions;   

DOI  :  10.1016/j.jalgebra.2012.12.019

来源: Elsevier

【 摘 要 】

We continue the program to make a moonshine path between a node of the extended E-8-diagram and the Monster. Our theory is a concrete model expressing some of the mysterious connections identified by John McKay, George Glauberman and Simon Norton. In this article, we treat the 3A- and 6A-nodes. We determine the orbits of triples (x, y, z) in the Monster where z is an element of 2B, x, y is an element of 2A boolean AND C(z) and xy is an element of 3A boolean OR 6A. Such x, y correspond to a rootless EE8-pair in the Leech lattice. For the 3A and 6A cases, we shall say something about the half Weyl groups, which are proposed in the Glauberman-Norton theory. Most work in this article is with lattices, due to their connection with dihedral subgroups of the Monster. These lattices are M + N, where M, N is the relevant pair of EE8-sublattices, and their annihilators in the Leech lattice. The isometry groups of these four lattices are analyzed. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free