Mathematical Research Letters

Volume 21 (2014)

Number 4

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

Pages: 757 – 779



M. Iovanov (Department of Mathematics, University of Iowa, Iowa City, Ia., U.S.A.; and Department of Mathematics, University of Bucharest, Romania)

G. Mason (Department of Mathematics, University of California at Santa Cruz, Calif., U.S.A.)

S. Montgomery (Department of Mathematics, University of Southern California, Los Angeles, Calif., U.S.A.)


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.

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