McKay Correspondence Extends E6, E7, E8 to Sporadic Groups via VOAs — E8 Intelligence Research

FINDING: McKay correspondence links finite subgroups of SL(2,C) to affine Dynkin diagrams of types E6, E7, E8, and extends to sporadic groups via vertex operator algebras (VOAs). | MATH: Finite subgroups of SL(2,C) correspond to ADE Dynkin diagrams (An, Dn, E6, E7, E8). McKay's E7 observation: dihedral subgroups of the Baby Monster sporadic group correspond to subalgebras of the Baby Monster VOA with central charge c=7/10. McKay's E6 observation: analogous correspondence for the largest Fischer group Fi24'. Key constants: central charge c=7/10 (related to minimal model Virasoro algebra), Coxeter numbers for E6 (12), E7 (18), E8 (30). | CONNECTION: Root systems of E6, E7, E8 have Coxeter numbers 12, 18, 30 — ratios 12:18:30 = 2:3:5, linked to golden ratio via 5-fold symmetry (E8 contains H4, the 600-cell symmetry). The golden ratio φ = (1+√5)/2 ≈ 1.618 appears in E8's root system norms. Base-60 emerges from 12×5 = 60, 18×3.333... = 60, 30×2 = 60. | DEPTH: 9 — Profound unification of fin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com