Multistrand Eigenvalue conjecture and Racah symmetries

TL;DR

This paper explores symmetries of Racah matrices derived from the eigenvalue conjecture, focusing on multistrand braids in quantum algebras, which could simplify understanding these complex matrices.

Contribution

It investigates Racah matrix symmetries based on the eigenvalue conjecture specifically for multistrand braids, advancing the theoretical understanding of quantum algebra representations.

Findings

Identifies new symmetries of Racah matrices from the eigenvalue conjecture

Provides insights into the relation between Racah and R-matrices for multistrand braids

Enhances the theoretical framework for quantum algebra computations

Abstract

Racah matrices of quantum algebras are of great interest at present time. These matrices have a relation with $\mathcal{R}$-matrices, which are much simpler than the Racah matrices themselves. This relation is known as the eigenvalue conjecture. In this paper we study symmetries of Racah matrices which follow from the eigenvalue conjecture for multistrand braids.