Algebraic Proof of the Symmetric Space Theorem

TL;DR

This paper provides an elementary algebraic proof of the symmetric space theorem, simplifying the original proof by avoiding complex quark-model constructions.

Contribution

It introduces a more accessible algebraic approach to proving the symmetric space theorem, making the result more understandable.

Findings

Elementary algebraic proof of the symmetric space theorem

Simplifies previous complex proofs

Enhances understanding of symmetric space structures

Abstract

I give a relatively elementary proof of the symmetric space theorem, due to Goddard, Nahm and Olive \cite{GNO}. Unlike their original proof, which involves the quark-model construction, I only use elementary algebraic techniques.