On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

TL;DR

This paper develops a canonical irreducible representation for orthofermion algebra, demonstrating how all representations decompose, and explores the implications for orthosupersymmetric systems, revealing their connection to parasupersymmetry and fractional supersymmetry.

Contribution

It introduces a canonical irreducible representation for arbitrary order orthofermion algebra and links orthosupersymmetry to parasupersymmetry and fractional supersymmetry.

Findings

All representations decompose into canonical or trivial forms.

Orthosupersymmetric systems of order p have parasupersymmetry of order p.

Orthosupersymmetric systems of order p have fractional supersymmetry of order p+1.

Abstract

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.