Abstract
We present an expanded and detailed discussion of the mathematical tools required to cull and filter representations of the Coxeter Group BC 4 into providing bases for the construction of minimal off-shell representations of the 4D, \( \mathcal{N} \) = 1 spacetime supersymmetry algebra.
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D.E.A. Gates and S.J. Gates Jr., A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1 Spacetime SUSY Representations, arXiv:1601.00725 [INSPIRE].
M. Faux and S.J. Gates Jr., Adinkras: A Graphical technology for supersymmetric representation theory, Phys. Rev. D 71 (2005) 065002 [hep-th/0408004] [INSPIRE].
S.J. Gates Jr. and L. Rana, A Theory of spinning particles for large-N extended supersymmetry, Phys. Lett. B 352 (1995) 50 [hep-th/9504025] [INSPIRE].
S.J. Gates Jr. and L. Rana, A Theory of spinning particles for large-N extended supersymmetry. 2., Phys. Lett. B 369 (1996) 262 [hep-th/9510151] [INSPIRE].
B. Bollobás, Modern Graph Theory, Springer (1998), p. 52.
S.J. Gates Jr., The Search for Elementarity Among Off-Shell SUSY Representations, KIAS Newsl. 5 (2012) 19.
S.J. Gates Jr., T. Hübsch and K. Stiffler, Adinkras and SUSY Holography: Some explicit examples, Int. J. Mod. Phys. A 29 (2014) 1450041 [arXiv:1208.5999] [INSPIRE].
S.J. Gates Jr., T. Hübsch and K. Stiffler, On Clifford-algebraic dimensional extension and SUSY holography, Int. J. Mod. Phys. A 30 (2015) 1550042 [arXiv:1409.4445] [INSPIRE].
M. Calkins, D.E.A. Gates, S.J. Gates Jr. and K. Stiffler, Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence, Int. J. Mod. Phys. A 30 (2015) 1550050 [arXiv:1501.00101] [INSPIRE].
S.J. Gates Jr. et al., A Lorentz covariant holoraumy-induced “gadget” from minimal off-shell 4D, \( \mathcal{N} \) = 1 supermultiplets, JHEP 11 (2015) 113 [arXiv:1508.07546] [INSPIRE].
I. Chappell II, S.J. Gates Jr. and T. Hübsch, Adinkra (in)equivalence from Coxeter group representations: A case study, Int. J. Mod. Phys. A 29 (2014) 1450029 [arXiv:1210.0478] [INSPIRE].
H.S.M. Coxeter, Discrete groups generated by reflections, Ann. Math. 35 (1934) 588.
N. Bourbaki, Elements of Mathematics. Lie Groups and Lie Algebras. Chapters 4-6, Springer (2002) [ISBN: 978-3-540-42650-9] [Zbl 0983.1700.1].
S.J. Gates Jr., W.D. Linch III and J. Phillips, When superspace is not enough, hep-th/0211034 [UMDEPP-02-054] [CALT-68-2387] [INSPIRE].
F. Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, Druck und Verlag von B.G. Teubner, Leipzig Germany (1884), reprinted as F. Klein, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, 2nd rev. ed., Dover, New York U.S.A. (1956) (English translation).
G. Arfken, Mathematical Methods for Physicists, 3rd ed., Academic Press, Orlando FL U.S.A. (1985), pp. 184-185 and 239-240.
S.J. Gates Jr. and K. Stiffler, Adinkra ‘Color’ Confinement In Exemplary Off-Shell Constructions Of 4D, \( \mathcal{N} \) = 2 Supersymmetry Representations, JHEP 07 (2014) 051 [arXiv:1405.0048] [INSPIRE].
S.J. Gates Jr. and T. Hübsch, On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets, Adv. Theor. Math. Phys. 16 (2012) 1619 [arXiv:1104.0722] [INSPIRE].
K.M. Iga and Y.X. Zhang, Structural Theory and Classification of 2D Adinkras, Adv. High Energy Phys. 2016 (2016) 3980613 [arXiv:1508.00491] [INSPIRE].
K.M. Iga and Y.X. Zhang, private communication on Structural Theory and Classification of 2D Adinkras.
C.F. Doran et al., Codes and Supersymmetry in One Dimension, Adv. Theor. Math. Phys. 15 (2011) 1909 [arXiv:1108.4124] [INSPIRE].
C.F. Doran, M.G. Faux, S.J. Gates Jr., T. Hübsch, K.M. Iga and G.D. Landweber, Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry, arXiv:0806.0051 [UMDEPP-07-012-SUNY-O-663] [INSPIRE].
C.F. Doran et al., Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry, arXiv:0806.0050 [UMDEPP-08-010] [SUNY-O-667] [INSPIRE].
I. Chappell II et al., 4D, N = 1 Supergravity Genomics, JHEP 10 (2013) 004 [arXiv:1212.3318] [INSPIRE].
S.J. Gates Jr., J. Hallett, T. Hübsch and K. Stiffler, The Real Anatomy of Complex Linear Superfields, Int. J. Mod. Phys. A 27 (2012) 1250143 [arXiv:1202.4418] [INSPIRE].
S.J. Gates Jr., J. Hallett, J. Parker, V.G.J. Rodgers and K. Stiffler, 4D, N = 1 Supersymmetry Genomics (II), JHEP 06 (2012) 071 [arXiv:1112.2147] [INSPIRE].
S.J. Gates Jr., T. Hübsch, K.M. Iga and S. Mendez-Deis, N = 4 and N = 8 SUSY Quantum Mechanics and Klein’s Vierergruppe, in preparation.
S.J. Gates Jr. et al., 4D, N = 1 Supersymmetry Genomics (I), JHEP 12 (2009) 008 [arXiv:0902.3830] [INSPIRE].
C. Doran, K.M. Iga, J. Kostiuk, G. Landweber and S. Méndez-Diez, private communication on Geometrization of N -Extended 1-Dimensional Supersymmetry Algebras, I.
C. Doran, K.M. Iga, J. Kostiuk, G. Landweber and S. Méndez-Diez, Geometrization of N -extended 1-dimensional supersymmetry algebras, I, Adv. Theor. Math. Phys. 19 (2015) 1043 [arXiv:1311.3736] [INSPIRE].
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Gates, D.E.A., Gates, S.J. & Stiffler, K. A proposal on culling & filtering a coxeter group for 4D, \( \mathcal{N} \) = 1 spacetime SUSY representations: revised. J. High Energ. Phys. 2016, 76 (2016). https://doi.org/10.1007/JHEP08(2016)076
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DOI: https://doi.org/10.1007/JHEP08(2016)076