On two geometric theta lifts

Bruinier, J.; Funke, J.

Abstract

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. In this paper we establish for the orthogonal group O(p,2) an adjointness result between Borcherds's singular theta lift and the Kudla-Millson lift. We extend this result to arbitrary signature by introducing a new singular theta lift for O(p,q). On the geometric side, this lift can be interpreted as a differential character, in the sense of Cheeger and Simons, for the cycles under consideration.

Citation

Bruinier, J., & Funke, J. (2004). On two geometric theta lifts. Duke Mathematical Journal, 125(1), 45-90. https://doi.org/10.1215/s0012-7094-04-12513-8

• Journal Article Type: Article
• Publication Date: Jan 1, 2004
• Deposit Date: Aug 27, 2008
• Publicly Available Date: Aug 27, 2008
• Journal: Duke Mathematical Journal
• Print ISSN: 0012-7094
• Publisher: Duke University Press
• Peer Reviewed: Peer Reviewed
• Volume: 125
• Issue: 1
• Pages: 45-90
• DOI: https://doi.org/10.1215/s0012-7094-04-12513-8