Super Weyl Groups via Directed Coxeter Graphs for Lie Superalgebras — E8 Intelligence Research

FINDING: Super Weyl groups for basic classical Lie superalgebras are defined via Coxeter graphs with directed edge labeling to encode odd root parity, generalizing Weyl groups to supersymmetric root systems. | MATH: Coxeter graph with directed edges for odd roots; quotient of Coxeter group by relations from odd root parity; root system decomposition into even (bosonic) and odd (fermionic) roots; Cartan matrix modified by parity signs. | CONNECTION: Root systems of Lie superalgebras extend crystallographic Coxeter-Dynkin diagrams (e.g., A(m|n), B(m|n), D(m|n), etc.) preserving Weyl group structure but with directed edges marking odd simple roots; ratios 0.618, 1.618 appear in quantum group deformations of these superalgebras; base-60 not directly present but root system symmetries relate to hexagonal/triangular lattices (e.g., A₂ root system). | DEPTH: 8 — This formalizes the symmetry group of supersymmetric physical theories, linking Coxeter group theory to supergravity and string theo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com