Modular invariance and (quasi)-Galois symmetry in conformal field theory

A brief heuristic explanation is given of recent work with Juergen Fuchs, Beatriz Gato-Rivera and Christoph Schweigert on the construction of modular invariant partition functions from Galois symmetry in conformal field theory. A generalization, which we call quasi-Galois symmetry, is also described. As an application of the latter, the invariants of the exceptional algebras at level g (for example Es level 30) expected from conformal embeddings are presented. (orig.)