  Let $\mathcal{O}_q(G)$ be the quantized algebra of regular functions on a
semisimple simply connected compact Lie group $G$. Simple unitarizable left
$\mathcal{O}_q(G)$-module are classified.
  In this article, we compute their Gelfand-Kirillov dimension where $G$ is of
the type $A$, $C$ and $D$.
