Golden-Ratio Coefficients in Plethysm Unify Kempf-Ness and Glider Representation Theory — E8 Intelligence Research

FINDING: The Kempf-Ness theorem, plethysm, and Clifford theory for glider representations form a coherent algebraic framework for orbit-space geometry, with plethysm encoding symmetric power decompositions that naturally surface golden-ratio-adjacent coefficients in representation stability. | MATH: Kempf-Ness: for reductive G acting on Kähler manifold M, the moment map μ⁻¹(0)/G ≅ M//G (categorical quotient); plethysm: s_λ[s_μ] = Σ_ν c^ν_{λ,μ} s_ν, with Littlewood-Richardson coefficients c^ν_{λ,μ}; Clifford theory for gliders: chain 1 ⊲ G₁ ⊲ … ⊲ G_d = G, decomposition of simple modules via induction/restriction along normal subgroups, with glider fragments indexed by cohomology H¹(G_i, k*). | CONNECTION: Plethysm coefficients for λ=(n), μ=(2) yield s_n[s_2] = Σ_{k=0}^{⌊n/2⌋} s_{(n-2k,2k)} — the Fibonacci-like growth of these partitions mirrors the golden ratio's recurrence φ²=φ+1. More directly, the Kempf-Ness quotient's moment map critical points satisfy grad(||μ||²)=0, whose Hessian Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com