Skip to main content

Research Repository

Advanced Search

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

Funke, Jens; Hofmann, Eric

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


Authors

Eric Hofmann



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.

Citation

Funke, J., & Hofmann, E. (2021). The construction of Green currents and singular theta lifts for unitary groups. Transactions of the American Mathematical Society, 374(4), 2909-2947. https://doi.org/10.1090/tran/8289

Journal Article Type Article
Acceptance Date Aug 25, 2020
Online Publication Date Jan 27, 2021
Publication Date 2021
Deposit Date Sep 1, 2020
Publicly Available Date Sep 16, 2020
Journal Transactions of the American Mathematical Society
Print ISSN 0002-9947
Electronic ISSN 1088-6850
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 374
Issue 4
Pages 2909-2947
DOI https://doi.org/10.1090/tran/8289
Related Public URLs https://arxiv.org/abs/1903.00262

Files





You might also like



Downloadable Citations