Ikeda lifts form a distinguished subspace of Siegel modular forms. In this paper we prove several global and local results concerning this space. We find that degenerate principal series representations (for the Siegel parabolic) of the symplectic group Sp2n of even degree satisfy a Hecke duality relation which has applications to Ikeda lifts and leads to converse theorems. Moreover we apply certain differential operators to study pullbacks of Ikeda lifts.
Bibliographical noteFunding Information:
The research of the second author was supported by the German University of Technology in Oman , by Research stays at the Max-Planck-Institute of Mathematics in Bonn in 2011 and 2013, and the Graduiertenkolleg Experimentelle und konstruktive Algebra at the RWTH Aachen.
© 2014 Elsevier Inc.
- Automorphic L-functions
- Degenerate principal series
- Differential operators
- Ikeda lifts