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Adinkra (in)equivalence from Coxeter group representations: A case study
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| Organization: | Center for String and Particle Theory, Department of Physics, University of Maryland |
| Organization: | Department of Physics & Astronomy, Howard University |
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| International Journal of Modern Physics A |
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Using a MathematicaTM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the GR(4, 4) algebra, closely related to the N = 1 (simple) supersymmetry algebra in four-dimensional space–time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these GR(4, 4) representations into three suggestive classes.
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