Galois self-dual cuspidal types and Asai local factors

Anandavardhanan, U. K., Kurinczuk, Rob, Matringe, Nadir, Sécherre, Vincent and Stevens, Shaun (2021) Galois self-dual cuspidal types and Asai local factors. Journal of the European Mathematical Society, 23 (9). 3129–3191. ISSN 1435-9855

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Abstract

Let F=Fo be a quadratic extension of non-archimedean locally compact fields of odd residual characteristic and σ be its non-trivial automorphism. We show that any σ-self-dual cuspidal representation of GLn.F/ contains a σ-self-dual Bushnell-Kutzko type. Using such a type, we construct an explicit test vector for Flicker's local Asai L-function of a GLn.Fo/-distinguished cuspidal representation and compute the associated Asai root number. Finally, by using global methods, we compare this root number to Langlands-Shahidi's local Asai root number, and more generally we compare the corresponding epsilon factors for any cuspidal representation.

Item Type:	Article
Additional Information:	Funding Information: Vincent Sécherre was partially supported by the Institut Universitaire de France. Shaun Stevens was partially supported by the Heilbronn Institute for Mathematical Research.
Uncontrolled Keywords:	asai local factor,distinction,root number,test vector,type theory,mathematics(all),applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1807.07755
Depositing User:	LivePure Connector
Date Deposited:	12 Apr 2019 08:30
Last Modified:	28 Mar 2025 09:16
URI:	https://ueaeprints.uea.ac.uk/id/eprint/70544
DOI:	10.4171/JEMS/1080

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