On Two Geometric Theta Lifts

Details On Two Geometric Theta Lifts On Two Geometric Theta Lifts

2002-12-20

arxiv.org/abs/math/0212286v4

Mathematics

Number Theory

35 pages

Scientific paper

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. In this paper, we establish for O(p,2) an adjointness result between Borcherds' singular theta lift and the Kudla-Millson theta lift. We extend this result to arbitrary signature by introducing a new Borcherds 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.

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