Regge symmetry of 6j-symbols of the Lorentz group

TL;DR

This paper derives new symmetries and expressions for 6j-symbols of the Lorentz group, specifically for unitary principal series representations of SL(2,C), including an analogue of Regge symmetry.

Contribution

It introduces novel symmetry properties and explicit expressions for 6j-symbols of the Lorentz group, expanding understanding of their mathematical structure.

Findings

Derived new symmetry for 6j-symbols of SL(2,C)

Established an analogue of Regge symmetry for these symbols

Provided new explicit expressions for the symbols

Abstract

In this paper we derive new symmetry and new expression for $6j$-symbols of the unitary principal series representations of the $SL(2,\mathbb{C})$ group. This allowed us to derive for them the analogue of the Regge symmetry.