Supergroup Chern-Simons Hilbert Space Dimension Linked to Coxeter and Weyl Invariants — E8 Intelligence Research

FINDING: Hilbert space dimension in supergroup Chern-Simons theory is linked to Coxeter group order and Weyl group invariants, with combinatorial quantization revealing root system structure. | MATH: For gauge supergroup G, Hilbert space dimension = |W|⁻¹ Σw∈W det(1 - w)ᵈ, where W is Weyl group, d = rank; Coxeter number h appears in level shift k → k + h∨; dimension formula involves quantum factorial (q-deformed) for root system. | CONNECTION: Coxeter group order |W| = ∏ (m_i + 1) for exponents m_i; root system ratios (e.g., 1.618 for E₈) appear in quantum dimensions; base-60 emerges in finite group Chern-Simons via modular data (SL(2,Z) action). | DEPTH: 7 — Directly ties topological quantum field theory to discrete symmetry groups (Coxeter/Weyl), with explicit dimension formulas that mirror crystallographic root system structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com