Braid group representations from twisted quantum doubles of finite groups

Abstract. We investigate the braid group representations arising from cate-gories 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 cor-responding pure braid group representations factor through a finite p-group, which answers a question asked of the first author by V. Drinfeld. 1