Adinkras From Ordered Quartets of BC${}_4$ Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget

Abstract

We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: $-1/3$, $1/3$, or $1$ and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.

arXiv commentLaTeX twice, 56pp, 30 tables, 5 figures, latest version includes link to updated code, minor corrections, and additional support about inequivalent representations and tetrahedral geometry comments added along with observations about similarity with results previously found by Nekrasov

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Cited by in corpus (6)

• Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\ell$- and $\tilde{\ell }$-Equivalence Classes
• Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras
• Adinkras From Ordered Quartets of BC4 Coxeter Group Elements and Regarding Another Gadget's 1,358,954,496 Matrix Elements
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras
• Examples of 4D, N = 2 Holoraumy
• 4D, $\mathcal{N}=1$ Matter Gravitino Genomics