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Session S16 - Quantum symmetries

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Tambara-Yamagami Categories over the Reals: The Non-Split Case

Sean Sanford

Indiana University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In 1998, Daisuke Tambara and Shigeru Yamagami investigated a simple set of fusion rules, and proved under which circumstances those rules could be given a coherent associator. This elementary yet difficult computation remains an outlier in the subject, as such associators are rarely computed by hand.

In this project, we are investigating a generalization of such fusion rules to the setting where the simple objects are no longer required to be absolutely simple. Over the real numbers, this means that objects are either real, complex or quaternionic. This flexibility has interesting implications that we will explore through a series of examples.

Joint work with Julia Plavnik (Indiana University) and Dalton Sconce (Indiana University).

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