On some properties of quantum doubles of finite groups

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 SN⋉AN, where A is a finite abelian group. A proof of this result for A=1 appears in a paper by Iovanov, Montgomery, and Mason. 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 by Eric Rowell.