On representations of semidirect products of a compact quantum group with a finite group

TL;DR

This paper classifies all irreducible unitary representations of semidirect products of a compact quantum group with a finite group, describing conjugates and fusion rules.

Contribution

It provides a complete classification of irreducible representations and fusion rules for these semidirect product quantum groups, advancing understanding of their structure.

Findings

Classification of all irreducible unitary representations

Description of conjugate representations

Fusion rules for the semidirect product

Abstract

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible unitary representations in terms of this classification, and the fusion rules for the semidirect product.