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July 27, 2026Open Access

Coxeter Groups Bridge Root Symmetries and Quantum Topological Invariants — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Overview

This research demonstrates connections between Coxeter groups and quantum invariants, suggesting significant implications for mathematical physics.

Key Points

  • Explore the relationship between Coxeter groups, root system symmetries, and quantum topological invariants.
  • Analysis of Coxeter numbers and their implications for root systems.
  • Mathematical formulations relating quantum groups to modular data.
  • Examination of the excess function for Coxeter groups.
  • Coxeter numbers identified for several groups: A_n (3), D_n (4), E_6 (6), E_7 (12), E_8 (30).
  • Demonstrated encoding of root system symmetries into quantum invariants via modular S-matrix.
  • Established a condition for roots of unity linking Coxeter numbers and quantum groups.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a67009540bca442e0d4a694https://doi.org/10.5281/zenodo.21545357
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  1. 1Coxeter Groups Link Root Symmetries to Quantum S-Matrices — E8 Intelligence Research2026
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  5. 5Spectral Gap of Coxeter Elements Tied to Coxeter Number via Cartan Matrices — E8 Intelligence Research2026