Refining the classification of the irreps of the 1D N-Extended Supersymmetry

TL;DR

This paper classifies the irreducible representations of 1D N-Extended Supersymmetric Quantum Mechanics, focusing on their connectivity and providing a detailed classification for N up to 8.

Contribution

It refines the classification of irreducible representations by introducing connectivity as a key feature, extending previous classifications up to N=8.

Findings

Classification of irreps with same fields content but different connectivity

Introduction of a connectivity symbol to encode graph information

Extended classification results up to N=8

Abstract

The linear finite irreducible representations of the algebra of the 1D $N$-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The classification of the irreducible representations with the same fields content and different connectivity is presented up to $N\leq 8$.