Gelfand-Kirillov dimension of some simple unitarizable modules

TL;DR

This paper classifies simple unitarizable modules over quantized function algebras on certain Lie groups and computes their Gelfand-Kirillov dimensions for types A, C, and D.

Contribution

It provides the first explicit computation of Gelfand-Kirillov dimensions for these modules in types A, C, and D.

Findings

Classification of simple unitarizable modules

Explicit Gelfand-Kirillov dimension calculations for types A, C, D

Enhanced understanding of module structure over quantum groups

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 $D$.