Braid group representations from twisted quantum doubles of finite groups

Pavel Etingof, Eric Rowell and Sarah Witherspoon

Vol. 234 (2008), No. 1, 33–41

DOI: 10.2140/pjm.2008.234.33

Abstract

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite groups, in contrast to the categories associated with quantum groups at roots of unity. We also show that in the case of p-groups, the corresponding pure braid group representations factor through a finite p-group, which answers a question asked of the first author by V. Drinfeld.

Keywords

twisted quantum doubles, Artin’s braid group, pure braid group, representations, modular categories

Mathematical Subject Classification 2000

Primary: 16W30

Secondary: 20F36, 18D10

Milestones

Received: 9 March 2007

Published: 1 January 2008