The branching rules of conformal embeddings

After recalling the main properties of a conformal embedding of Lie algebrasgp, which is defined by the equality of the Sugawara central charges on both sides, we launch a systematic study of their branching rules. The bulk of the paper is devoted to the proof of a general formula in the casesu(mn)₁su(m)_nsu(n)_m. At the end we give some applications to the construction of modular invariant partition functions.