Degenerate Whittaker functions for Sp_n(R)
Bruinier, J.; Funke, J.; Kudla, S.
Professor Jens Funke email@example.com
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) .
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|
|Publisher||Oxford University Press|
|Peer Reviewed||Peer Reviewed|
Accepted Journal Article
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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