Representations of quantum SU(2) operators on a local chart

TL;DR

This paper constructs Hilbert space representations of quantum SU(2) using local charts composed of tensor products of functions on a quantum disc and a classical circle, detailing the actions of algebra generators and derivatives.

Contribution

It introduces a novel method for representing quantum SU(2) operators on a local chart framework involving tensor products of quantum and classical function spaces.

Findings

Explicit Hilbert space representations of quantum SU(2) constructed.

Actions of generators and derivatives explicitly computed.

Provides a foundation for further analysis of quantum group representations.

Abstract

Hilbert space representations of quantum SU(2) by multiplication operators on a local chart are constructed, where the local chart is given by tensor products of square integrable functions on a quantum disc and on the classical unit circle. The actions of generators of quantum SU(2), generators of the opposite algebra, and noncommutative partial derivatives are computed on a Hilbert space basis.