McKay Correspondence: Golden Ratio Links Binary Icosahedral Group to E8 Lie Algebra — E8 Intelligence Research

Abstract

FINDING: McKay correspondence links E8 Lie algebra to binary icosahedral group via golden ratio, unifying finite group theory with exceptional Lie symmetry. | MATH: Binary icosahedral group order = 120, E8 Coxeter number = 30, golden ratio φ = (1+√5)/2 ≈ 1.618; character values involve φ and its conjugate φ' = (1-√5)/2 ≈ -0.618; McKay graph of E8 affine Dynkin diagram has eigenvalues 2cos(π/h) with h=30. | CONNECTION: Direct geometric link: icosahedral symmetry (order 60 rotational, 120 binary) encodes φ in its rotation angles (arccos(φ/2) ≈ 36°, 72°); E8 root system (240 roots) projects to icosahedron vertices; golden ratio appears in character table entries (e.g., 2cos(π/5)=φ). | DEPTH: 9 — This is a profound unification of finite group theory (binary icosahedral), exceptional Lie algebra (E8), and the golden ratio, revealing a deep symmetry underlying both discrete and continuous mathematical structures. The McKay correspondence is a cornerstone of modern mathematics, linking ADE cl Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com