A theory of Miyawaki liftings: The Hilbert-Siegel case

Abstract

The Miyawaki liftings are defined by the pullbacks of Ikeda liftings. Recently, Ikeda and Yamana extended the theory of Ikeda liftings. 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.

arXiv comment51 pages. We extended the local results to the case of almost tempered unitary representations, and added an application to the local Gan-Gross-Prasad conjecture

Cited by in corpus (2)

• Automorphic forms for some even unimodular lattices
• Non-vanishing of Miyawaki type lift