One rational expression in Vogel parameters computes quantum dimensions of Cartan powers of adjoint and X2 representations for many simple Lie algebras, though it vanishes in some cases where the representation exists.
Landsberg and L.Manivel, A universal dimension formula for co mplex simple Lie algebras
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On universal quantum dimensions of certain two-parameter series of representations
One rational expression in Vogel parameters computes quantum dimensions of Cartan powers of adjoint and X2 representations for many simple Lie algebras, though it vanishes in some cases where the representation exists.