Tambara-Yamagami, loop groups, bundles and KK-theory

Evans, David E. and Gannon, Terry 2023. Tambara-Yamagami, loop groups, bundles and KK-theory. Advances in Mathematics 421 , 109002. 10.1016/j.aim.2023.109002

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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, generalising 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 respectively.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0001-8708
Funders:	EPSRC
Date of First Compliant Deposit:	23 March 2023
Date of Acceptance:	18 March 2023
Last Modified:	04 Jul 2024 08:44
URI:	https://orca.cardiff.ac.uk/id/eprint/157915

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