FSZ-groups and Frobenius-Schur Indicators of Quantum Doubles

2012/08/21 by Iovanov, Miodrag, Mason, Geoffrey, Montgomery, Susan
#20C99 #FOS: Mathematics #Group Theory (math.GR) #Primary 20D99 #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Secondary 16T05

paper · doi:10.48550/arxiv.1208.4153

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, PSL₂(q), M₁₁, M₁₂ and regular nilpotent groups. However we show there is an irregular nilpotent group of order 5⁶ with non-integer indicators.

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