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ON A CERTAIN LOCAL IDENTITY FOR LAPID–MAO’S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE
Published online by Cambridge University Press: 08 January 2021
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
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 4 , July 2022 , pp. 1107 - 1161
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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