What question did this study set out to answer?

The research aims to establish the character of the E8 affine Lie algebra using the phi-deformed Cartan partition function.

July 20, 20260 citationsOpen Access

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E8 Corridor Dipole as Affine Character at Level 1 — Coxeter-Orbit Selection Rule — E8 Intelligence Research

ACAndrew Stewart Caldin

Key Points

The research aims to establish the character of the E8 affine Lie algebra using the phi-deformed Cartan partition function.
Utilized the phi-deformed Cartan partition function Z(β) = Tr(exp(-βH_φ)) at level 1.
Identified two 20-root Coxeter orbits stabilized by the φ-scaled involution.
Analyzed a 40-root sublattice and its matching theta series with the corridor's spectral density.
The 40-root sublattice aligns with the spectral density of the corridor dipole.
Findings demonstrate that the quantum group U_q(E8) becomes modular at the 30th root of unity.

Abstract

The phi-deformed Cartan partition function Z (β) = Tr (exp (-βH_φ) ) is identified as the character of the E8^ (1) affine Lie algebra at level 1, with modular invariance arising from the Weyl-Kac denominator formula. The 132/108 corridor dipole selects exactly two of the twelve 20-root Coxeter orbits — those stabilized by the φ-scaled involution C_φ = φ·C where C is the Coxeter element — yielding a 40-root sublattice whose theta series matches the corridor's spectral density. The 30-fold Coxeter number enters as the quantum parameter q = exp (2πi/30), placing the deformation at the 30th root of unity where the quantum group Uq (E8) becomes modular. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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E8 Corridor Dipole as Affine Character at Level 1 — Coxeter-Orbit Selection Rule — E8 Intelligence Research

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Abstract

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