A theory of Miyawaki liftings : the Hilbert-Siegel case

• Atobe, Hiraku

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.

Journal

• Mathematische annalen

  Mathematische annalen 376 (3-4), 1467-1535, 2020-04

  Springer

Keywords

• Primary 11F70
• Secondary 11F46

Details

• CRID: 1050287595684755968
• NII Article ID: 120007000857
• DOI: 10.1007/s00208-019-01946-w
• ISSN: 14321807
• ISSN: 00255831
• HANDLE: 2115/80775
• Web Site: http://link.springer.com/content/pdf/10.1007/s00208-019-01946-w.pdf
• Web Site: http://link.springer.com/article/10.1007/s00208-019-01946-w/fulltext.html
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN