Duke Mathematical Journal

On two geometric theta lifts

Jan Hendrik Bruinier and Jens Funke

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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.

Article information

Duke Math. J., Volume 125, Number 1 (2004), 45-90.

First available in Project Euclid: 25 September 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F27: Theta series; Weil representation; theta correspondences
Secondary: 11F55: Other groups and their modular and automorphic forms (several variables)


Bruinier, Jan Hendrik; Funke, Jens. On two geometric theta lifts. Duke Math. J. 125 (2004), no. 1, 45--90. doi:10.1215/S0012-7094-04-12513-8. https://projecteuclid.org/euclid.dmj/1096128234

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