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Degenerate Whittaker functions for Sp_n(R)

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

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Authors

J. Bruinier

S. Kudla



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 Mar 28, 2024
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

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Accepted Journal Article (877 Kb)
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Copyright Statement
This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bruinier, J., Funke, J. & Kudla, S. (2018). Degenerate Whittaker functions for Sp_n(R). International Mathematics Research Notices 2018(1): 1-56 is available online at: https://doi.org/10.1093/imrn/rnw218.




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