Super Weyl Groups and Coxeter Graphs: Extending Lie Superalgebra Symmetry — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are a scattered mix of pedagogical videos (Pell's equation, Markov chains, continued fractions) and one substantive arXiv paper on super Weyl groups and Coxeter graphs — no unified "unsolvable competition problem" breakthrough is present. The core mathematical essence lies in the arXiv paper's extension of Weyl group/Coxeter machinery to Lie superalgebras.
MATH: - Pell equation: x2 − Dy2 = 1, solved via continued fraction convergents of √D. - Markov chain stationary vector π: π P = π, ∑ πi = 1. - Super Weyl group (arXiv 2401.11068): quotients of Weyl groups for basic classical Lie superalgebras; Coxeter graphs defined via sequences for fundamental root systems. Coxeter number h = order of product of simple reflections; for finite Weyl groups, h relates to eigenvalues of the Coxeter element as exp(2π i k/h). - No explicit new equation or constant extracted from the videos (they are expository).
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026super,
title = {{Super Weyl Groups and Coxeter Graphs: Extending Lie Superalgebra Symmetry — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446807},
url = {https://zenodo.org/records/23446807},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Super Weyl Groups and Coxeter Graphs: Extending Lie Superalgebra Symmetry — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446807
UR - https://zenodo.org/records/23446807
AB - FINDING: The search results are a scattered mix of pedagogical videos (Pell's equation, Markov chains, continued fractions) and one substantive arXiv paper on super Weyl groups and Coxeter graphs — no unified "unsolvable competition problem" breakthrough is present. The core mathematical essence lies in the arXiv paper's extension of Weyl group/Coxeter machinery to Lie superalgebras. MATH: - Pell equation: x^2 − Dy^2 = 1, solved via continued fraction convergents of √D. - Markov chain stationary vector π: π P = π, ∑ π_i = 1. - Super Weyl group (arXiv 2401.11068): quotients of Weyl groups for basic classical Lie superalgebras; Coxeter graphs defined via sequences for fundamental root systems. Coxeter number h = order of product of simple reflections; for finite Weyl groups, h relates to eigenvalues of the Coxeter element as exp(2π i k/h). - No explicit new equation or constant extracted from the videos (they are expository). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -