Diagonal lattices and rootless $EE_8$ pairs

Autor:	Griess, Jr., Robert L., Lam, Ching Hung
Rok vydání:	2011
Předmět:	Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	Let E be an integral lattice. We first discuss some general properties of an SDC lattice, i.e., a sum of two diagonal copies of E in E \bot E. In particular, we show that its group of isometries contains a wreath product. We then specialize this study to the case of E = E_8 and provide a new and fairly natural model for those rootless lattices which are sums of a pair of EE_8-lattices. This family of lattices was classified in [7]. We prove that this set of isometry types is in bijection with the set of conjugacy classes of rootless elements in the isometry group O(E_8), i.e., those h \in O(E_8) such that the sublattice (h - 1)E_8 contains no roots. Finally, our model gives new embeddings of several of these lattices in the Leech lattice. Comment: this article has been submitted
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1101.2188 Zobrazit plný text záznamu View this record from Arxiv