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Session S16 - Quantum symmetries

Friday, July 16, 12:45 ~ 13:10 UTC-3

Doubly-rational finite groups

Andrew Schopieray

Pacific Institute for the Mathematical Sciences/University of Alberta, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

As a young student of algebra, one might be happy to discover that the character tables of some finite groups consist only of integers. These are sometimes known as rational groups. There are many sporadic results in the classification of rational groups but it very much remains an open area of inquiry. In this talk we will discuss the search for quantum doubles of finite groups whose (generalized) character tables consist only of integers. It would be sensible to call these doubly-rational groups. Our task is a strict subset of the classical problem of characterizing rational groups, but also a strict subset of the modern problem of characterizing certain modular tensor categories. As such, this talk should be of interest to a broad audience.

Joint work with Terry Gannon (University of Alberta).

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