  In radial quantization, the ground states of a gauge theory on ADE
singularities $R^4/\Gamma$ are characterized by flat connections that are maps
from $\Gamma$ to the gauge group. We study Class S theory of type $A_1$ on a
Riemann surface of genus $g>1$, without punctures. The fundamental building
block of Class S theory is the trifundamental Trinion theory - a low energy
limit of two M5 branes compactified on the three-punctured Riemann sphere. We
show through the superconformal index, that the supersymmetric Casimir energy
of the trifundamental theory imposes a constraint on the set of allowed flat
connections, which agrees with the prediction of a duality relating the ground
state Hilbert space of Class S on ADE singularities to the Hilbert space of a
certain dual Chern-Simons theory whose gauge group is given by the McKay
correspondence. The conjecture is shown to hold for $\Gamma=Z_k$, agreeing with
the previous results of Benini et al. and Alday et al. Non-abelian
generalizations of this duality are analyzed by considering the example of the
dicyclic group Dic${}_2$, corresponding to gauge group SO$(8)$.
