Computing Higher Indicators for the Double of a Symmetric Group

Abstract

In this paper we explicitly determine all indicators for the Drinfel'd doubles of the symmetric group acting upon up to 10 objects. We explore when distinct characters give exactly the same indicators and when the indicators have a zero value. We find that the indicators are all non-negative integers, which supports our conjecture that the indicators for the Drinfel'd double of any symmetric group will be non-negative integers, just as they are for the symmetric groups themselves.