On two geometric theta lifts

2004/10/01 by Jan Hendrik Bruinier, Jens Funke · 27 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology

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

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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