On two geometric theta lifts

2004/10/01 by Jan Hendrik Bruinier, Jens Funke · 418 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Computer science #Geometric and Algebraic Topology #Geometry #Lift (data mining) #Mathematical analysis #Mathematics #Pure mathematics #Signature (topology) #Type (biology)

paper · pdf · doi:10.1215/s0012-7094-04-12513-8

published in Duke Mathematical Journal 125(1) (Duke University Press)

openalex publication_date 2004/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• On modular forms associated with indefinite quadratic forms of signature (2,n?2)

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