Quite a character: The spectrum of Yang–Mills on S3S3

We introduce a simple method to extract the representation content of the spectrum of a system with SU(2)SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4)SO(2,4) symmetry, such as conformal field theories in four dimensions. As a specific application we obtain an explicit generating function for the representation content of free planar Yang–Mills theory on S3S3. The extension to N=4N=4 super-Yang–Mills is also discussed.