5 problems

Twining-character modular transformation conjecture. The matrix entries satisfy

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…

Let $k,n$ be integers and let … be the Wigner $6j$ symbol appearing in the description of the cubic invariant $\mathscr{P}_{n,3}(F)$. Nonvanishing conjecture. For every pair of int…

The $SU(2)$ $6j$ symbol is considered in the large-spin asymptotic regime, with spins $j_i$ and corresponding dihedral angles $\theta_i$. Let … The coefficients $A_n$ denote consec…