English

$FSZ$-groups and Frobenius-Schur Indicators of Quantum Doubles

Rings and Algebras 2012-08-22 v1 Group Theory Quantum Algebra

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.

Keywords

Cite

@article{arxiv.1208.4153,
  title  = {$FSZ$-groups and Frobenius-Schur Indicators of Quantum Doubles},
  author = {Miodrag Iovanov and Geoffrey Mason and Susan Montgomery},
  journal= {arXiv preprint arXiv:1208.4153},
  year   = {2012}
}

Comments

17 pages