The dual folding of the Lie algebra has recently appeared in our work arXiv:2103.06044 on twisted 6d (2,0) superconformal quantum field theories on circle. The 6d (2,0) theories of A, D, E type are not a gauge theory nor have any Lagrangian description. These theories arise in type IIB string on A,D,E singularities. The work contains a lot of calculation of the related elliptic genus, which could play some role in the representation theory. Our work also contains the folding of $A_{2r}$ theories to $C'_r$.
Kimyeong Lee
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