Unitary Continuous Representations of Compact Quantum Groups

TL;DR

This paper extends the concept of continuous representations to compact quantum groups, showing that such unitary correpresentations decompose into finite-dimensional irreducibles, generalizing classical group representation theory.

Contribution

It introduces a framework for unitary continuous correpresentations of compact quantum groups and proves their decomposition into finite-dimensional irreducible components.

Findings

Unitary continuous correpresentations decompose into finite-dimensional irreducibles

Generalization of classical representation theory to quantum groups

Framework applicable to $C^*$-completions of Hopf algebras

Abstract

Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is proved that the unitary continuous correpresentations decompose in finite dimensional irreducible correpresentations.