Adinkra (in) equivalence from Coxeter group representations: A case study
Abbreviated Journal Title
Int. J. Mod. Phys. A
Quantum mechanics; supersymmetry; off-shell supermultiplets; N-EXTENDED SUPERSYMMETRY; SPINNING PARTICLES; Physics, Nuclear; Physics, Particles & Fields
Using a Mathematica(TM) code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4x4 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 S-4 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.
International Journal of Modern Physics A
"Adinkra (in) equivalence from Coxeter group representations: A case study" (2014). Faculty Bibliography 2010s. 5155.