Regge symmetry of 6-j or super 6-jS symbols: a re-analysis with partition properties

TL;DR

This paper re-analyzes the Regge symmetry of 6-j and super 6-j symbols, revealing new partition properties and providing tools for exact computation, with implications for symmetry reduction in super symbols.

Contribution

It introduces new stable partitions based on Regge transformations for 6-j and super 6-j symbols, enhancing understanding of their symmetry properties and computational methods.

Findings

Five Regge transformations act as a spectrometric splitter.

Four new stable partitions S4(0), S4(1), S(2), S4(5) identified.

Super Regge symmetry reduces only for beta parity, with some partitions vanishing.

Abstract

It shown that the five Regge transformations act as a spectrometric splitter on any 6-j symbol. Four unknown partitions are brought out: S4(0), S4(1), S(2) and S4(5). They are stable subsets, with well defined parameters depending only on triangles and quadrangles. These findings are easily generalized to super 6-jS symbols, properly labelled by their own parity alpha, beta, gamma. Super Regge symmetry is reduced only for beta where S4(2), S4(5) vanish. In addition, all tools for computing exact values of any 6-jS are provided.