Evans, David E. and Gannon, Terry 2020. Tambara-Yamagami, loop groups, bundles and KK-theory. arXiv |
|
PDF
- Submitted Pre-Print Version
Download (672kB) | Preview |
Abstract
This paper is part of a sequence interpreting quantities of conformal field theories K-theoretically. Here we give geometric constructions of the associated module categories (modular invariants, nimreps, etc). In particular, we give a KK-theory interpretation of all modular invariants for the loop groups of tori, as well as most known modular invariants of loop groups. In addition, we find unexpectedly that the Tambara-Yamagami fusion category has an elegant description as bundles over a groupoid, and use that to interpret its module categories as KK-elements. We establish reconstruction for the doubles of all Tambara-Yamagami categories, generalizing work of Bischoff to even-order groups. We conclude by relating the modular group representations coming from finite groups and loop groups to the Chern character and to the Fourier-Mukai transform
Item Type: | Article |
---|---|
Date Type: | Published Online |
Status: | Submitted |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Funders: | EPSRC |
Last Modified: | 27 Mar 2020 08:41 |
URI: | http://orca.cf.ac.uk/id/eprint/130573 |
Actions (repository staff only)
![]() |
Edit Item |