  The role played by the Euler anomaly in the dictionary relating sphere
partition functions of four dimensional theories of class $\mathcal{S}$ and two
dimensional nonrational CFTs is clarified. On the two dimensional side, this
involves a careful treatment of scale factors in Liouville/Toda correlators.
Using ideas from tinkertoy constructions for Gaiotto duality, a framework is
proposed for evaluating these scale factors. The representation theory of Weyl
groups plays a critical role in this framework.
