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A local converse theorem for Archimedean GL(n)

  • Moshe Adrian and Shuichiro Takeda EMAIL logo
Published/Copyright: March 31, 2023

Abstract

We prove a local converse theorem for GL n over the Archimedean local fields which characterizes an infinitesimal equivalence class of irreducible admissible generic representations of GL n ( ) or GL n ( ) in terms of twisted local gamma factors.

MSC 2020: 20G05

Communicated by Freydoon Shahidi


Funding source: Simons Foundation

Award Identifier / Grant number: 422638

Award Identifier / Grant number: 584704

Funding statement: The first-named author was partially supported by the Simons Foundation Collaboration Grant 422638 and by a PSC-CUNY award, jointly funded by the Professional Staff Congress and The City University of New York. The second-named author was partially supported by the Simons Foundation Collaboration Grant 584704.

Acknowledgements

We thank Hervé Jacquet for suggesting this problem. We also thank the anonymous referee for his/her valuable comments.

References

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Received: 2022-08-06
Revised: 2022-12-28
Published Online: 2023-03-31
Published in Print: 2023-05-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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