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On two geometric theta lifts

2004; Duke University Press; Volume: 125; Issue: 1 Linguagem: Inglês

10.1215/s0012-7094-04-12513-8

1547-7398

Jan Hendrik Bruinier, Jens Funke,

Geometric and Algebraic Topology

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.