Coxeter Groups Unify Root Symmetries and Quantum S-Matrices — E8 Intelligence Research

July 27, 2026Open Access

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Key Points

This research explores how Coxeter groups unify root-system symmetries and quantum group modular S-matrices at roots of unity.
Analysis of Coxeter groups and their properties, focusing on E8 and H4 root systems
Calculation of modular S-matrix entries using a simplified mathematical framework
Investigation of the relationships between Coxeter numbers and quantum field theories
Coxeter number for E8 is 30, revealing connections to base-60 structure.
Golden ratio c appears in H4's non-crystallographic Coxeter group, indicating c-scaling in its edges.
Modular S-matrix unitarity yields mathematical constants relating to Weyl groups, confirming theoretical predictions for E8.

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Investigates quantum group modular S-matrices in finite groups, highlighting symmetry connections.

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Andrew Stewart Caldin (2026) studied this question.

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