Weyl Groups and Tutte Polynomials in Hyperplane Arrangement Invariants — E8 Intelligence Research

FINDING: Weyl group action on hyperplane arrangements provides the structural backbone for enumerative geometry invariants, with Tutte polynomial specializations encoding combinatorial symmetry. | MATH: Weyl groups = finite reflection groups generated by simple reflections \(s_i\) with relations \((s_i s_j)^{mᵢⱼ}=1\), \(mᵢⱼ∈\{2,3,4,6\}\) (crystallographic condition); hyperplane arrangement \(A\) in \(R^n\) with characteristic polynomial \(χA(t)=∑ₖ₌₀^n (-1)^k b_k tⁿ⁻ᵏ\); Tutte polynomial \(TA(x,y)=∑A (x-1)r(A)-r(A)(y-1)|A|-r(A)\); Okounkov's framework links these to quantum cohomology via equivariant K-theory, with structure constants given by \(Nd_1,d_2d_3 = ∫_{M̄0,3(X,d)} ev^*(α_1∪α_2∪α_3)\). | CONNECTION: The crystallographic condition \(mᵢⱼ∈\{2,3,4,6\}\) directly yields root system angles — \(90^∘, 60^∘, 45^∘, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com