Symmetries of the Kac-Peterson modular matrices of affine algebras

G2quivers

“…So these were the cases for Calabi-Yau orbifolds, now we have G 2 -orbifolds and M-theory; could there be similar relations to g 2 WZW models? Indeed, some exceptional cases for the latter model were found at levels 3 and 4 [36] while the complete classification is still in want; could these perhaps be in correspondence with the quivers thus far presented?…”

Automorphism modular invariants of current algebras

“…This work follows [17], where the automorphism invariants for algebra A m1 ⊕ · · · ⊕ A ms were treated. Our restriction here to simple Lie algebras is convenient, but as [17] shows, the generalization to semi-simple Lie algebras should be possible. It is hoped that classification results like ours will teach us something about more general classes of conformal field theories, perhaps all rational ones.…”

“…A section 6 is inserted that contains the relevant analysis for B ℓ,2 and D ℓ,2 . For completeness, we include the results (but not the proofs) for the A ℓ series [17].…”

The Automorphisms of Affine Fusion Rings

“…Nevertheless, the two problems are related. The automorphism invariants for the affine algebras were classified in [17,18]; a lemma proved there (our Proposition 4.1 below) involving q-dimensions will be very useful to us, and conversely the arguments in Section 4 of this paper could be used to considerably simplify the proofs of [17,18].…”

“…Their automorphisms appear explicitly for instance in the classification of modular invariant (i.e., torus) partition functions [17,18], and also in D-branes and boundary conditions for conformal field theory (see, e.g., [1]). For instance, fusionautomorphisms (more generally, -homomorphisms) generate large classes of nonnegative integer representations of the fusion-ring, each of which is associated to a boundary (cylinder) partition function.…”