# Spacetime Spin and Chirality Operators for Minimal 4D, $\cal N$ = 1 Supermultiplets From BC${}_4$ Adinkra-Tessellation of Riemann Surfaces

## TL;DR

This paper introduces a mathematical framework using Riemann surface tessellations and Coxeter group adinkras to derive spacetime chirality and Lorentz generators for minimal 4D, $ ext{N}=1$ supermultiplets.

## Contribution

It presents a novel geometric construction linking Riemann surface tessellations with supersymmetry representations in four dimensions.

## Key findings

- Spacetime chirality emerges from the tessellation structure.
- Lorentz generators are constructed via Coxeter group symmetries.
- The approach offers a new perspective on supermultiplet geometry.

## Abstract

We propose an explicit mathematical construction and plausibility arguments for how spacetime chirality and Lorentz generators emerge for minimal, off-shell 4D, $\cal N$ = 1 supermultiplets by use of a 4.4.4.4 tesselation of Riemann surfaces based on plaquettes originating from Coxeter Group BC${}_4$ adinkras.