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01 February 2006 Lifting automorphic representations on the double covers of orthogonal groups
Daniel Bump, Solomon Friedberg, David Ginzburg
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Duke Math. J. 131(2): 363-396 (01 February 2006). DOI: 10.1215/S0012-7094-06-13126-5


Suppose that G and H are connected reductive groups over a number field F and that an L-homomorphism ρ:LGLH is given. The Langlands functoriality conjecture predicts the existence of a map from the automorphic representations of G(A) to those of H(A). If the adelic points of the algebraic groups G, H are replaced by their metaplectic covers, one may hope to specify an analogue of the L-group (depending on the cover), and then one may hope to construct an analogous correspondence. In this article, we construct such a correspondence for the double cover of the split special orthogonal groups, raising the genuine automorphic representations of SO~2k(A) to those of SO~2k+1(A). To do so, we use as integral kernel the theta representation on odd orthogonal groups constructed by the authors in a previous article [3]. In contrast to the classical theta correspondence, this representation is not minimal in the sense of corresponding to a minimal coadjoint orbit, but it does enjoy a smallness property in the sense that most conjugacy classes of Fourier coefficients vanish


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Daniel Bump. Solomon Friedberg. David Ginzburg. "Lifting automorphic representations on the double covers of orthogonal groups." Duke Math. J. 131 (2) 363 - 396, 01 February 2006.


Published: 01 February 2006
First available in Project Euclid: 12 January 2006

zbMATH: 1107.11024
MathSciNet: MR2219245
Digital Object Identifier: 10.1215/S0012-7094-06-13126-5

Primary: 11F70
Secondary: 11F27 , 22E50 , 22E55

Rights: Copyright © 2006 Duke University Press


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Vol.131 • No. 2 • 01 February 2006
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