Representation Category of Free Wreath Product of Classical Groups

TL;DR

This paper constructs a specific rigid $C^*$-tensor category whose associated quantum group is the free wreath product of classical groups, advancing the understanding of quantum symmetries.

Contribution

It introduces a new concrete $C^*$-tensor category framework for analyzing free wreath products of classical groups.

Findings

Successfully reconstructs the quantum group via Woronowicz--Tannaka--Krein duality.

Provides a concrete categorical model for free wreath products.

Enhances the understanding of quantum symmetries in classical groups.

Abstract

In this paper, we construct a rigid concrete $C^*$-tensor category whose associated compact quantum group, reconstructed via Woronowicz--Tannaka--Krein duality, is the free wreath product of classical groups.