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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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Preservation of depth in the local geometric Langlands correspondence
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by Tsao-Hsien Chen and Masoud Kamgarpour PDF
Trans. Amer. Math. Soc. 369 (2017), 1345-1364 Request permission


It is expected that, under mild conditions, the local Langlands correspondence preserves depths of representations. In this article, we formulate a conjectural geometrisation of this expectation. We prove half of this conjecture by showing that the depth of a categorical representation of the loop group is greater than or equal to the depth of its underlying geometric Langlands parameter. A key ingredient of our proof is a new definition of the slope of a meromorphic connection, a definition which uses opers.
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Additional Information
  • Tsao-Hsien Chen
  • Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
  • Email:
  • Masoud Kamgarpour
  • Affiliation: School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland 4072, Australia
  • Email:
  • Received by editor(s): November 24, 2014
  • Received by editor(s) in revised form: January 8, 2015, and July 22, 2015
  • Published electronically: July 20, 2016

  • Dedicated: To Volodya Drinfeld, on the occasion of his sixtieth birthday
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1345-1364
  • MSC (2010): Primary 17B67, 17B69, 22E50, 20G25
  • DOI:
  • MathSciNet review: 3572276