Adinkra (in) equivalence from Coxeter group representations: A case study

    Authors

    I. Chappell; S. J. Gates;T. Hubsch

    Comments

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    Abbreviated Journal Title

    Int. J. Mod. Phys. A

    Keywords

    Quantum mechanics; supersymmetry; off-shell supermultiplets; N-EXTENDED SUPERSYMMETRY; SPINNING PARTICLES; Physics, Nuclear; Physics, Particles & Fields

    Abstract

    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.

    Journal Title

    International Journal of Modern Physics A

    Volume

    29

    Issue/Number

    6

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    24

    WOS Identifier

    WOS:000332522400003

    ISSN

    0217-751X

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