{"paper":{"title":"Moonshine paths for 3A and 6A nodes of the extended E8-diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.QA","authors_text":"Ching Hung Lam, Robert L. Griess Jr.","submitted_at":"2012-05-28T01:53:37Z","abstract_excerpt":"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 $z\\in 2B$, $x, y \\in 2A \\cap C(z)$ and $xy\\in 3A \\cup 6A$. Such $x, y$ correspond to a rootless $EE_8$-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 Gla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6017","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}