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A theory of Miyawaki liftings : the Hilbert-Siegel case
| Title: | A theory of Miyawaki liftings : the Hilbert-Siegel case |
| Authors: | Atobe, Hiraku Browse this author →KAKEN DB |
| Keywords: | Primary 11F70 | | Secondary 11F46 |
| Issue Date: | Apr-2020 |
| Publisher: | Springer |
| Journal Title: | Mathematische annalen |
| Volume: | 376 |
| Issue: | 3-4 |
| Start Page: | 1467 |
| End Page: | 1535 |
| Publisher DOI: | 10.1007/s00208-019-01946-w |
| Abstract: | 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. |
| Rights: | 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 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/80775 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 跡部 発
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