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The construction of Green currents and singular theta lifts for unitary groups.

Funke, Jens and Hofmann, Eric (2021) 'The construction of Green currents and singular theta lifts for unitary groups.', Transactions of the American Mathematical Society., 374 (4). pp. 2909-2947.

Abstract

With applications in the Kudla program in mind we employ singular theta lifts for the reductive dual pair $ \mathrm {U}(p,q)\times \mathrm {U}(1,1)$ to construct two different kinds of Green forms for codimension $ q$-cycles in Shimura varieties associated to unitary groups. We establish an adjointness result between our singular theta lift and the Kudla-Millson lift. Further, we compare the two Greens forms and obtain modularity for the generating function of the difference of the two Green forms. Finally, we show that the Green forms obtained by the singular theta lift satisfy an eigenvalue equation for the Laplace operator and conclude that our Green forms coincide with the ones constructed by Oda and Tsuzuki by different means.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/tran/8289
Publisher statement:This paper is available under a Creative Commons CC-BY-NC-ND licence.
Date accepted:25 August 2020
Date deposited:02 September 2020
Date of first online publication:27 January 2021
Date first made open access:16 September 2020

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