2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108851Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius algebras in C. Such an algebra A encodes all data needed to ensure the existence of correlators of a local conformal field theory. The Picard group of the category of A-bimodules has a physical interpretation, too: it describes internal symmetries of the conformal field theory, and allows one to identify generalized Kramers-Wannier dualities of the theory. When applying these general results to concrete models based on affine Lie algebras, a detailed knowledge of certain representations of the modular group is needed. We discuss a conjecture that relates these representations to those furnished by twining characters of affine Lie algebras.12 pages, submitted to the proceedings of a conference in honor of Robert L. Wilson and James LepowskyQuantum AlgebraCategory Theory81T40;18D10;18D35;81T45text