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

Shuichiro Takeda

Type: Article

Publication Date: 2011-01-01

Citations: 8

DOI: https://doi.org/10.1515/crelle.2011.053

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).

Locations

arXiv (Cornell University) - View - PDF
Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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+	A Regularized Siegel-Weil Formula: The First Term Identity	1994	Stephen S. Kudla Stephen Rallis
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+ PDF Chat	The nonarchimedean theta correspondence for $\mathrm {GSp}(2)$ and $\mathrm {GO}(4)$	1999	Brooks Roberts
+ PDF Chat	The multiplicity-one theorem for generic automorphic forms of GSp(4)	2007	David D. Jiang David Soudry
+	Structure Arising from Induction and Jacquet Modules of Representations of Classical p-Adic Groups	1995	Marko Tadić
+	On the Howe correspondence for symplectic–orthogonal dual pairs	2005	Annegret Paul
+ PDF Chat	Canonical Extensions of Harish-Chandra Modules to Representations of <i>G</i>	1989	W. Casselman