Degenerate Whittaker functions for Sp_n(R)

Bruinier, J.; Funke, J.; Kudla, S.

Abstract

In this paper, we construct Whittaker functions with exponential growth for the degenerate principal series of the symplectic group of genus n induced from the Siegel parabolic subgroup. This is achieved by explicitly constructing a certain Goodman–Wallach operator which yields an intertwining map from the degenerate principal series to the space of Whittaker functions, and by evaluating it on weight- ℓ standard sections. We define a differential operator on such Whittaker functions which can be viewed as generalization of the ξ -operator on harmonic Maass forms for \SL2(\R) .

Citation

Bruinier, J., Funke, J., & Kudla, S. (2018). Degenerate Whittaker functions for Sp_n(R). International Mathematics Research Notices, 2018(1), 1-56. https://doi.org/10.1093/imrn/rnw218

• Journal Article Type: Article
• Acceptance Date: Aug 29, 2016
• Online Publication Date: Nov 2, 2016
• Publication Date: Jan 3, 2018
• Deposit Date: Nov 23, 2016
• Publicly Available Date: Nov 2, 2017
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2018
• Issue: 1
• Pages: 1-56
• DOI: https://doi.org/10.1093/imrn/rnw218