Duke Mathematical Journal

On two geometric theta lifts

Jan Hendrik Bruinier and Jens Funke

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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.

Article information

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

Dates
First available in Project Euclid: 25 September 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1096128234

Digital Object Identifier
doi:10.1215/S0012-7094-04-12513-8

Mathematical Reviews number (MathSciNet)
MR2097357

Zentralblatt MATH identifier
02135351

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

Citation

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


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