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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Let E/F 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 GL(n,E) contains a σ-self-dual Bushnell–Kutzko type. Using such a type, we cons- truct an explicit test vector for Flicker’s local Asai L-function of a GL(n,F)-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
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
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Depositing User: LivePure Connector
Date Deposited: 12 Apr 2019 08:30
Last Modified: 24 May 2023 03:44
DOI: 10.4171/JEMS/1080

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