Explicit computation of quantum-group F-matrices

Determine explicit formulas for the F-matrices, equivalently the \(6j\)-symbols, associated with quantum groups beyond the cases for which they are currently known, using the conformal-block and Fuchsian-ODE formalism developed for rational conformal field theories.

Background

The paper notes that F-matrices for rational conformal field theories with affine Kac–Moody symmetry are related to $6j$-symbols of the corresponding quantum groups. Although the proposed method is developed primarily for Virasoro minimal models, the authors suggest applying it to extended rational conformal field theories, including affine Kac–Moody theories.

The unresolved issue is that explicit expressions for these quantum-group F-matrices or $6j$-symbols are not available for all quantum groups. The paper presents the proposed formalism as a possible independent computational approach to obtaining them.

References

The F-matrices in these cases are related to the $6j$-symbols for the corresponding quantum group. These are not known explicitly for all quantum groups, and our formalism might provide an independent way to compute them.

— Conformal blocks and braiding matrices for RCFTs I: Virasoro minimal models  (2609.19904 - Govindarajan et al., 17 Sep 2026) in Section 6, “Conclusion and discussion”