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Let $\mathcal{O}_q(G)$ be the quantized algebra of regular functions on asemisimple 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 ofthe type $A$, $C$ and $D$.

Gelfand-Kirillov dimension of some simple unitarizable modules