Open Collections

Modular data for centres

Banff International Research Station for Mathematical Innovation and Discovery

The classification of small index subfactors has resulted in the discovery of some rather unusual fusion categories. Those coming from the extended Haagerup subfactor seem particularly interesting --- at this point we know of no relationship to any family or standard construction. As part of the effort to understand these unusual objects, we have computed the modular data for the centres of these fusion categories. As it turns out, we need to know remarkably little about the fusion categories; the conditions on modular data are so restrictive that we can leverage information about the Galois action and the representation theory of SL(2,Z) to completely determine the modular data. Time permitting, I'll indicate the range of examples we've since tested these techniques against.

Mathematics; Category theory; homological algebra; Quantum theory; Algebraic structures

video/mp4

Author affiliation: Australian National University

2017-02-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60610

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/