Kronecker Coefficient Complexity Bounds Depend on Partition Shape Parameters — E8 Intelligence Research

FINDING: Kronecker coefficients \(g(λ,μ,ν)\) — central to Geometric Complexity Theory (GCT) — resist efficient computation; explicit complexity bounds depend on partition shape parameters, with hook-like cases (small second part \(M\)) yielding tractable regimes. | MATH: Kronecker coefficient \(g(λ,μ,ν) = (S^λ ⊗ S^μ ⊗ S^ν)GL_n\) (triple tensor product invariant multiplicity). Complexity bounds: \(\) (number of parts), \(N\) (largest part), \(M\) (smallest second part). When \(M = O(1)\) (hook-like), computation is polynomial-time; general case suspected #P-hard. Plethysm coefficients \(p_λ(μ)\) similarly hard. GCT uses orbit closure separation: \(GL_n · [_n]̄ ⊆ GL_n · [perm_n]̄\) to prove \(VP ≠ VNP\). | CONNECTION: The partitions \(λ,μ,ν\) index irreducible representations of \(GL_n\) — root systems of type \(Aₙ₋₁\). Hook-like partitions corres Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com