Mapping class group representations from Drinfeld doubles of finite groups

Understand

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point.

• We obtain concrete descriptions of such representations in terms of finite group data.
• This allows us to establish various properties of these representations.
• In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.