Quasi-Galois symmetries of the modular $S$-matrix

The recently introduced Galois symmetries of rational conformal field theory are generalized, for the case of WZW theories, to “quasi-Galois symmetries.” These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrixS, including some that previously had been observed empirically. In addition, quasi-Galois symmetries allow us to construct modular invariants and to relateS-matrices as well as modular invariants at different levels. They also lead us to a convenient closed expression for the branching rules of the conformal embeddings g ~ so(dim g)