The versatility of the Drinfeld double of a finite group

TL;DR

This survey explores the diverse roles of the Drinfeld double of finite groups and their representations across various mathematical and physical contexts, highlighting its significance in multiple research areas.

Contribution

It provides a comprehensive review of the applications and importance of the Drinfeld double of finite groups in harmonic analysis, Lie algebras, quantum groups, and related fields.

Findings

The Drinfeld double connects finite group theory with quantum algebra.

Applications span harmonic analysis, non-commutative geometry, and Verlinde formula.

The survey highlights the versatility and research relevance of the Drinfeld double.

Abstract

In this survey we review different instances in which the Drinfeld double of a finite group and its representations play a role, touching upon some of Tom Koornwinder's research interests: harmonic analysis, Lie algebras, quantum groups, non-commutative geometry, and Verlinde formula.