Quantum groups from stationary matrix models

TL;DR

This paper investigates stationary quantum groups represented through matrix models, providing general results, numerous examples, and an in-depth analysis of quantum permutation groups.

Contribution

It introduces the concept of stationary models for quantum groups and explores their properties with extensive examples and detailed case studies.

Findings

Stationary models characterize certain quantum groups via Haar integration.

The paper provides a comprehensive list of examples of stationary quantum groups.

A detailed analysis is conducted specifically on quantum permutation groups.

Abstract

We study the quantum groups appearing via models $C(G)\subset M_K(C(X))$ which are "stationary", in the sense that the Haar integration over $G$ is the functional $tr\otimes\int_X$. Our results include a number of generalities, notably with a substantial list of examples, and a detailed discussion in the quantum permutation group case.