N=4 and N=8 SUSY Quantum Mechanics and Klein's Vierergruppe

TL;DR

This paper explores the structure of signed permutation matrices satisfying specific algebraic relations, revealing their connection to Klein's Vierergruppe and confirming previous computational counts within a broader mathematical framework.

Contribution

It demonstrates that certain signed permutation matrices form cosets of Klein's Vierergruppe, providing a theoretical validation of earlier computational results and extending the analysis to other algebraic groups.

Findings

Signed permutation matrices form cosets of Klein's Vierergruppe.

Verification of previous computational counts from 2012.

Extension of analysis to other algebraic groups like GR(1,1), GR(2,2), and GR(8,8).

Abstract

Sets of signed permutation matrices satisfying the GR(4,4) algebra are shown to be, up to sign, left cosets of Klein's famous Vierergruppe. In this way we verify the count done by computer in 2012, and set it in a more significant mathematical context. A similar analysis works for GR(1,1), GR(2,2) and GR(8,8).