Multistrand eigenvalue conjecture and Racah symmetries

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.