Non-simply Laced McKay Correspondence and Triality

Abstract

The classical McKay correspondence establishes a one-to-one correspondence between finite subgroups of SU (2) and simply-laced root systems, namely root systems of ADE type. In this article, we extend the McKay correspondence to all root systems, simply-laced or not, and relate this correspondence to triality of quaternions.

ADE Bundles over Surfaces

“…This particular form is given in [42] and its generalization for non-simply laced G is given in [43,44]. Such a correspondence was originally motivated from the duality between F-theory and heterotic string theory in physics by the work of Friedman-Morgan-Witten [24] and Donagi [20] where different proofs of this correspondence are also given.…”