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Type: Journal article
Title: Group dualities, T-dualities, and twisted K-theory
Author: Varghese, M.
Rosenberg, J.
Citation: Journal of the London Mathematical Society, 2018; 97(1):1-23
Publisher: Oxford University Press
Issue Date: 2018
ISSN: 0024-6107
Statement of
Varghese Mathai and Jonathan Rosenberg
Abstract: This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on H3 induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the Segal spectral sequence, giving simpler computations of certain twisted K-theory groups of compact Lie groups relevant for D-brane charges in WZW theories and rank-level dualities. Finally we study a duality for orientifolds based on complex Lie groups with an involution.
Keywords: 19L50 (primary); 81T30; 57T10 (secondary)
Description: Published online 15 November 2017
Rights: © 2017 London Mathematical Society
RMID: 0030078531
DOI: 10.1112/jlms.12085
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Appears in Collections:Mathematical Sciences publications

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