A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1 Spacetime SUSY Representations

TL;DR

This paper reviews mathematical methods to select and organize Coxeter group representations for constructing minimal off-shell supersymmetry representations in four-dimensional spacetime, highlighting the emergence of Lorentz symmetry from one-dimensional structures.

Contribution

It introduces a novel approach to cull and filter Coxeter group representations for supersymmetry, emphasizing the emergence of Lorentz symmetry in a new mathematical framework.

Findings

Mathematical tools for culling Coxeter group representations

Mechanism for emergent Lorentz symmetry in adinkras

Framework for constructing 4D, N=1 supersymmetry representations

Abstract

We review 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, $ {\cal N}$ = 1 spacetime supersymmetry algebra. Of necessity this includes a description of the mathematical mechanism by which four dimensional Lorentz symmetry appears as an emergent symmetry in the context of one dimensional adinkras with four colors described by the Coxeter Group $BC_4$.