# What are the quantum dimensions of the primary fields for SU(N) level k Kac-Moody current algebras?

The CFT of the $\mathrm{SU}(N)$ 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 $\mathrm{SU}(2)$ level $k$ Kac-Moody current algebra, there is a general expression for the quantum dimensions of the $\mathrm{SU}(2)$ primary fields.