Theta lifting for tempered representations of real unitary groups

We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as cohomologically induced representations in the weakly fair range. Th...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 398; p. 108188
Main Author Ichino, Atsushi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 26.03.2022
Subjects
Real unitary groups
Theta lifting
Real unitary groups
Theta lifting
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Summary:We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as cohomologically induced representations in the weakly fair range. This extends a result of J.-S. Li in the case of discrete series representations with sufficiently regular infinitesimal character, whose theta lifts can be expressed as cohomologically induced representations in the good range.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108188