Journal article

A nonabelian Fourier transform for tempered unipotent representations

Abstract:: We define an involution on the elliptic space of tempered unipotent representations of inner twists of a split simple p-adic group G and investigate its behaviour with respect to restrictions to reductive quotients of maximal compact open subgroups. In particular, we formulate a precise conjecture about the relation with a version of Lusztig’s nonabelian Fourier transform on the space of unipotent representations of the (possibly disconnected) reductive quotients of maximal compact subgroups. We give evidence for the conjecture, including proofs for SL_n and PGL_n.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Aubert, A.-M., Ciubotaru, D., & Romano, B. (2024). A nonabelian Fourier transform for tempered unipotent representations. Compositio Mathematica, 161(1), 13–73.

MLA Style

Aubert, A.-M., et al. “A Nonabelian Fourier Transform for Tempered Unipotent Representations.” Compositio Mathematica, vol. 161, no. 1, Cambridge University Press, 2024, pp. 13–73.

Chicago Style

Aubert, A-M, D Ciubotaru, and B Romano. 2024. “A Nonabelian Fourier Transform for Tempered Unipotent Representations.” Compositio Mathematica 161 (1): 13–73.
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Files:: Aubert_et_al_2025_A_nonabelian_Fourier.pdf

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Publisher copy:: 10.1112/S0010437X24007401

Authors

+ Aubert, A-M More by this author

Role:: Author

+ Ciubotaru, D More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Romano, B More by this author

Role:: Author

Publisher:: Cambridge University Press
Journal:: Compositio Mathematica More from this journal
Volume:: 161
Issue:: 1
Pages:: 13-73
Publication date:: 2024-03-26
Acceptance date:: 2024-03-22
DOI:: 10.1112/S0010437X24007401
EISSN:: 1570-5846
ISSN:: 0010-437X

Language:: English
Keywords:: nonabelian Fourier transform

unipotent representations

elliptic representations

Langlands correspondence
Pubs id:: 1888433
Local pid:: pubs:1888433
Deposit date:: 2024-03-24

Terms of use

Copyright holder:: Aubert et al.
Copyright date:: 2025
Rights statement:: © The Author(s), 2025. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. Compositio Mathematica is © Foundation Compositio Mathematica.

Licence:: CC Attribution (CC BY)

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