Super Weyl Groups and Coxeter Graphs: Extending Lie Superalgebra Symmetry — E8 Intelligence Research
Year: 2026
Type: preprint
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: \(x^2 - Dy^2 = 1\), solved via continued fraction convergents of \(\sqrt{D}\). - Markov chain stationary vector \(\pi\): \(\pi P = \pi\), \(\sum \pi_i = 1\). - 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 \(\exp(2\pi i k/h)\). - 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
Author: Caldin, Andrew Stewart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222894497
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