open access

https://hdl.handle.net/2115/80775

A theory of Miyawaki liftings : the Hilbert-Siegel case

英語

Secondary 11F46

2020-04

Springer

Mathematische annalen

376(3-4)

1467-1535

The Miyawaki liftings are defined by the pullbacks of Ikeda liftings. Recently, Ikeda and Yamana extended the theory of Ikeda liftings to Hilbert-Siegel modular forms. In this paper, using their results, we establish a theory of Miyawaki liftings, both locally and globally. In the local theory, we describe the Miyawaki liftings for almost tempered unitary representations explicitly. In the global theory, we discuss the non-vanishing of the Miyawaki liftings using seesaw identities and the global Gan-Gross-Prasad conjecture. As an application of local Miyawaki liftings, we prove a new case of the local Gan-Gross-Prasad conjecture.

学術雑誌論文

Accepted Manuscript

This is a post-peer-review, pre-copyedit version of an article published in Mathematische Annalen. The final authenticated version is available online at: https://doi.org/10.1007/s00208-019-01946-w

0025-5831