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We calculate $q$-dimension of $k$-th Cartan power of fundamentalrepresentation $\Lambda_0$, corresponding to affine root of affine simply lacedKac-Moody algebras, and show that in the limit $q\rightarrow 1 $, and withnatural renormalization, it is equal to universal partition function ofChern-Simons theory on three-dimensional sphere.

Partition function of Chern-Simons theory as renormalized q-dimension