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Arthur packets for pure real forms of symplectic and special orthogonal groups

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  12 March 2025

Nicolas Arancibia Robert  and
Paul Mezo
Nicolas Arancibia Robert
Affiliation:
Laboratoire AGM - Analyse, Géométrie, Modélisation, CY Cergy Paris Université - site Saint Martin 2 av. Adolphe Chauvin 95302 Cergy-Pontoise Cedex, France e-mail: nicolas.arancibia-robert@cyu.fr
Paul Mezo*
Affiliation:
The School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada
*
e-mail: mezo@math.carleton.ca
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Abstract

Arthur packets have been defined for pure real forms of symplectic and special orthogonal groups following two different approaches. The first approach, due to Arthur, Moeglin, and Renard uses harmonic analysis. The second approach, due to Adams, Barbasch, and Vogan uses microlocal geometry. We prove that the two approaches produce essentially equivalent Arthur packets. This extends previous work of the authors and J. Adams for the quasisplit real forms.

Keywords

EndoscopyArthur packetsGroup representations

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The second author was supported in part by the NSERC grant RGPIN-06361.

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