Applications of Dynkin diagrams in Physics

Question

I was searching for applications of Dynkin Diagrams in physics and came across this site: https://ncatlab.org/nlab/show/McKay+correspondence but I can't quite understand how useful Dynkin diagrams are in the Yang-Mills theory. Can someone help me out?

I can't also understand how in this article https://arxiv.org/abs/1909.07993 ,they use Dynkin Diagrams to find the structure of the composite multi-monopoles, why do they do that?

What other applications Dynkin diagrams have in physics?

Thank you very much!