Conformal embeddings, rank-level duality and exceptional modular invariants (Q809172)

In Nucl. Phys. B 346, 349-386 (1990; see the preceding review) the author conjectured a way to get all the known modular invariants for all simple (affine) Kac-Moody algebras. Here it is verified in particular cases (e.g. an exceptional invariant for \({\mathfrak g}=su(2)\) at level 16 and so(q) at level 8 for \(q\geq 4)\). The branching rules of the conformal embeddings \(sp(2n)_ k\oplus sp(2k)_ n\subset so(4nk)_ 1\) (the subscript is the level) and \(so(r)_ q\oplus so(q)_ r\subset so(rq)_ 1\) for rq even are computed. - The knowledge of many a prerequisites is assumed.