The CFT of the SU(N) level k Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields. 


I know that, for SU(2) level k Kac-Moody current algebra, there is a general expression for the quantum dimensions of the SU(2) primary fields.



Quantum dimension in SU(N) level k Kac-Moody algebra
I found a nice database on Web. For example <https://www.math.ksu.edu/~gerald/voas/mtc/kmA3_3.html> list the data for SU(4) level 3 case.


