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# Mathematical Research Letters

## Volume 21 (2014)

### Number 4

### $FSZ$-groups and Frobenius-Schur indicators of quantum doubles

Pages: 757 – 779

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n4.a9

#### Authors

#### Abstract

We study the higher Frobenius-Schur indicators of the representations of the Drinfel’d double of a finite group $G$, in particular the question as to when all the indicators are integers. This turns out to be an interesting group-theoretic question. We show that many groups have this property, such as alternating and symmetric groups, $PSL_2 (q)$, $M_{11}$, $M_{12}$ and regular nilpotent groups. However, we show there is an irregular nilpotent group of order $5^6$ with non-integer indicators.

#### 2010 Mathematics Subject Classification

Primary 20Cxx, 20Dxx. Secondary 16T05.