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ON A CERTAIN LOCAL IDENTITY FOR LAPID–MAO’S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 January 2021

Kazuki Morimoto Open the ORCID record for Kazuki Morimoto [Opens in a new window]
Kazuki Morimoto*
Affiliation:
Department of Mathematics, Graduate School of Science, Kobe University, 1-1, Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan ([email protected])
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Abstract

Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients of automorphic forms on quasi-split reductive groups and metaplectic groups as an analogue of the Ichino–Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this article, we study the even unitary-group case. Indeed, we prove this local identity over p-adic fields. Further, we prove an equivalence between this local identity and a refined formal degree conjecture over any local field of characteristic zero. As a consequence, we prove a refined formal degree conjecture over p-adic fields and get an explicit formula of Whittaker–Fourier coefficients under certain assumptions.

Keywords

automorphic representationsspecial values of automorphic L-functionsrepresentation theory of p-adic reductive groups

MSC classification

Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 4 , July 2022 , pp. 1107 - 1161
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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