$EE_8$-lattices and dihedral groups

Details $EE_8$-lattices and dihedral groups $EE_8$-lattices and dihedral groups

2008-06-17

arxiv.org/abs/0806.2753v1

Mathematics

Representation Theory

87 pages, many figures

Scientific paper

We classify integral rootless lattices which are sums of pairs of $EE_8$-lattices (lattices isometric to $\sqrt 2$ times the $E_8$-lattice) and which define dihedral groups of orders less than or equal to 12. Most of these may be seen in the Leech lattice. Our classification may help understand Miyamoto involutions on lattice type vertex operator algebras and give a context for the dihedral groups which occur in the Glauberman-Norton moonshine theory.

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