Galois self-dual cuspidal types and Asai local factors

U.K. Anandavardhanan, Rob Kurinczuk, Nadir Matringe, Vincent Sécherre, Shaun Stevens

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Abstract

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.
Original languageEnglish
Pages (from-to)3129–3191
Number of pages61
JournalJournal of the European Mathematical Society
Volume23
Issue number9
Early online date4 May 2021
DOIs
Publication statusPublished - 2021

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