On some properties of quantum doubles of finite groups

2012/08/23 by Etingof, Pavel
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1208.4874

Abstract

We prove two results about quantum doubles of finite groups over the complex field. The first result is the integrality theorem for higher Frobenius-Schur indicators for wreath product groups S_N#A^N, where A is a finite abelian group. A proof of this result for A=1 appears in arXiv:1208.4153. The second result is a lower bound for the largest possible number of irreducible representations of the quantum double of a finite group with at most n conjugacy classes. This answers a question asked to me by Eric Rowell.

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