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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.

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I found a nice data base on Web. For example https://www.math.ksu.edu/~gerald/voas/mtc/kmA3_3.html list the data for SU(4) level 3 case.

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