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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk


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Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs

1Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, IN 47907-2067, USA

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2011, Issue 657, Pages 81–111, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2011.053, March 2011

Publication History

Received:
2008-12-11
Revised:
2010-04-20
Published Online:
2011-03-10

Abstract

Following the approach of B. Roberts, we characterize the non-vanishing of the global theta lift for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's work by a certain weaker assumption, and apply our results to small rank similitude groups. Among our applications is a certain instance of Langlands functorial transfer of a (non-generic) cuspidal automorphic representation of GSp(4) to GL(4).

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