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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An approach to the characterization of the local Langlands correspondence
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by Alexander Bertoloni Meli and Alex Youcis;
Represent. Theory 27 (2023), 415-430
DOI: https://doi.org/10.1090/ert/643
Published electronically: July 7, 2023

Abstract:

Scholze and Shin [J. Amer. Math. Soc. 26 (2013), pp. 261–294] gave a conjectural formula relating the traces on the automorphic and Galois sides of a local Langlands correspondence. Their work generalized an earlier formula of Scholze, which he used to give a new proof of the local Langlands conjecture for $\mathrm {GL}_n$. Unlike the case for $\mathrm {GL}_n$, the existence of non-singleton $L$-packets for more general reductive groups constitutes a serious representation-theoretic obstruction to proving that such a formula uniquely characterizes such a correspondence. We show how to overcome this problem, and demonstrate that the Scholze–Shin equation is enough, together with other standard desiderata, to uniquely characterize the local Langlands correspondence for discrete parameters.
References
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Bibliographic Information
  • Alexander Bertoloni Meli
  • Affiliation: Mathematics Department, University of Michigan, 530 Church St, Ann Arbor, Michigan 48109
  • MR Author ID: 1516552
  • Email: abertolo@umich.edu
  • Alex Youcis
  • Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
  • MR Author ID: 1528164
  • ORCID: 0000-0001-5000-6679
  • Email: ayoucis@g.ecc.u-tokyo.ac.jp
  • Received by editor(s): November 20, 2021
  • Received by editor(s) in revised form: January 6, 2023, and February 19, 2023
  • Published electronically: July 7, 2023
  • Additional Notes: During the completion of this work, the first author was partially funded by NSF RTG grant 1646385. The second author was partially supported by the funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 802787).
  • © Copyright 2023 Copyright by the authors
  • Journal: Represent. Theory 27 (2023), 415-430
  • MSC (2020): Primary 22E50; Secondary 11R39
  • DOI: https://doi.org/10.1090/ert/643
  • MathSciNet review: 4612310