Title

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

Authors

Authors

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

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

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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