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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Cayley and Langlands type correspondences for orthogonal Higgs bundles
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by David Baraglia and Laura P. Schaposnik PDF
Trans. Amer. Math. Soc. 371 (2019), 7451-7492 Request permission


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
  • MR Author ID: 912405
  • Email:
  • Laura P. Schaposnik
  • Affiliation: University of Illinois at Chicago, Chicago, Illinois 60607; and FU Berlin, 14195 Berlin, Germany
  • MR Author ID: 1013453
  • ORCID: 0000-0003-1417-2201
  • Email:
  • 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.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 7451-7492
  • MSC (2010): Primary 14D20, 14D21, 53C07; Secondary 14H70, 14P25
  • DOI:
  • MathSciNet review: 3939583