5 problems

Let $U=U\left[\begin{matrix}R_1&R_2\\R_3&R_4\end{matrix}\right]$ and…

Let $L=(\mathcal{\hat{R}}_1,\mathcal{\hat{R}}_2,\mathcal{\hat{R}}_3)$ and $L'=(\mathcal{\hat{R}}'_1,\mathcal{\hat{R}}'_2,\mathcal{\hat{R}}'_3)$ be triples of $\mathcal{\hat{R}}$-ma…

Let $R$ be a representation, and consider Racah matrices obtained from the tensor product $R\otimes R\otimes R$. Normalize each corresponding $\hat{\mathcal{R}}$-matrix so that the…

Eigenvalue conjecture. If the normalised $\mathcal{R}_1$ coincides with the normalised $\tilde{\mathcal{R}}_1$, then

Eigenvalue conjecture. Racah coefficients are fully defined by the set of normalised eigenvalues of the corresponding $\mathcal{R}$-matrices.