A brief history of hidden quantum symmetries in Conformal Field Theories

TL;DR

This paper reviews the development of hidden quantum symmetries in conformal field theories, emphasizing quantum groups and Coulomb gas methods, providing a historical overview and extensive references.

Contribution

It offers a concise historical review of quantum group symmetries in conformal field theories with focus on field theoretical representations and Coulomb gas techniques.

Findings

Quantum groups act as hidden symmetries in CFTs

Coulomb gas methods facilitate quantum group representations

Extensive bibliography supports the review

Abstract

We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods. An extensive bibliography is also included.