Representations of the compact quantum group $SU_q(N)$ and geometrical quantization

TL;DR

This paper applies geometrical quantization to construct infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(N)$, extending the method from $SU_q(2)$ to general $SU_q(n)$.

Contribution

It introduces a geometrical quantization approach for representing the algebra of functions on $SU_q(N)$, generalizing previous work from $SU_q(2)$ to higher dimensions.

Findings

Constructed infinite dimensional irreducible unitary representations for $SU_q(2)$.

Proposed a formulation of geometrical quantization for $SU_q(n)$.

Extended the method to general $SU_q(n)$ cases.

Abstract

The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the method for the general case $SU_q(n)$ is suggested. (This work is the English version of the article submitted for publication in Algebra Analiz.)