Gelfand-Kirillov dimension of some simple unitarizable modules

Abstract

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 $D$.

19 pages