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Transactions of the American Mathematical Society

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Cayley and Langlands type correspondences for orthogonal Higgs bundles


Authors: David Baraglia and Laura P. Schaposnik
Journal: Trans. Amer. Math. Soc. 371 (2019), 7451-7492
MSC (2010): Primary 14D20, 14D21, 53C07; Secondary 14H70, 14P25
DOI: https://doi.org/10.1090/tran/7587
Published electronically: November 5, 2018
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Abstract: Through Cayley and Langlands type correspondences, we give a geometric description of the moduli spaces of real orthogonal and symplectic Higgs bundles of any signature in the regular fibers of the Hitchin fibration. As applications of our methods, we complete the concrete abelianization of real slices corresponding to all quasi-split real forms, and we describe how extra components emerge naturally from the spectral data point of view.


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Additional Information

David Baraglia
Affiliation: School of Mathematical Sciences, The University of Adelaide, South Australia 5005, Australia
Email: david.baraglia@adelaide.edu.au

Laura P. Schaposnik
Affiliation: University of Illinois at Chicago, Chicago, Illinois 60607; and FU Berlin, 14195 Berlin, Germany
Email: schapos@uic.edu

DOI: https://doi.org/10.1090/tran/7587
Received by editor(s): October 10, 2017
Received by editor(s) in revised form: February 15, 2018, March 7, 2018, and April 4, 2018
Published electronically: November 5, 2018
Additional Notes: The first author was financially supported by the Australian Research Council Discovery Early Career Researcher Award DE160100024.
The second author was partially supported by the NSF grant DMS-1509693, the NSF CAREER Award DMS-1749013, and the Alexander von Humboldt Foundation.
The authors are thankful for financial support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties" (the GEAR Network), which financed several research visits during which the paper was written.
Article copyright: © Copyright 2018 American Mathematical Society