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Degenerate Whittaker functions for Sp_n(R).

Bruinier, J. and Funke, J. and Kudla, S. (2018) 'Degenerate Whittaker functions for Sp_n(R).', International mathematics research notices., 2018 (1). pp. 1-56.

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) .

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1093/imrn/rnw218
Publisher 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.
Date accepted:29 August 2016
Date deposited:28 November 2016
Date of first online publication:02 November 2016
Date first made open access:02 November 2017

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