Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/111405
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Type: | Journal article |
Title: | Group dualities, T-dualities, and twisted K-theory |
Author: | Varghese, M. Rosenberg, J. |
Citation: | Journal of London Mathematical Society, 2018; 97(1):1-23 |
Publisher: | Oxford University Press |
Issue Date: | 2018 |
ISSN: | 0024-6107 1469-7750 |
Statement of Responsibility: | 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 |
DOI: | 10.1112/jlms.12085 |
Grant ID: | http://purl.org/au-research/grants/arc/DP130103924 http://purl.org/au-research/grants/arc/DP150100008 |
Published version: | http://dx.doi.org/10.1112/jlms.12085 |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
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hdl_111405.pdf | Accepted version | 839.62 kB | Adobe PDF | View/Open |
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