On homomorphisms from finite subgroups of $SU(2)$ to Langlands dual pairs of groups

Yuki Kojima, Yuji Tachikawa

Let $N(\hat{I}“,G)$ be the number of homomorphisms from $\hat{I}“$ to $G$ up to conjugation by $G$. Physics of four-dimensional $\mathcal{N}=4$ supersymmetric gauge theories predicts that $N(Î…